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Tentukan nilai dari: a.

Pertanyaan

Tentukan nilai dari:

a. integral open parentheses x squared plus 3 over x close parentheses space text dx end text 

Pembahasan Soal:

Rumus integral tak tentu:

integral a x to the power of n space d x equals fraction numerator a over denominator n plus 1 end fraction x to the power of n plus 1 end exponent plus c

integral 1 over x space d x equals ln space open vertical bar x close vertical bar plus c

Integral pada soal di atas dapat ditentukan sebagai berikut.

integral open parentheses x squared plus 3 over x close parentheses space d x equals 1 third x cubed plus 3 space ln space open vertical bar x close vertical bar plus c

Dengan demikian, integral open parentheses x squared plus 3 over x close parentheses space d x equals 1 third x cubed plus 3 space ln space open vertical bar x close vertical bar plus c 

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

H. Eka

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Terakhir diupdate 05 Juni 2021

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Pertanyaan yang serupa

Tentukan nilai dari: b.

Pembahasan Soal:

Rumus integral tak tentu:

integral a x to the power of n space d x equals fraction numerator a over denominator n plus 1 end fraction x to the power of n plus 1 end exponent plus c

integral 1 over x space d x equals ln space open vertical bar x close vertical bar plus c

integral e to the power of x space d x equals e to the power of x plus c

Integral pada soal di atas dapat ditentukan sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell integral open parentheses fraction numerator 1 over denominator 2 x end fraction plus x squared minus e to the power of x close parentheses space d x end cell row blank equals cell integral open parentheses 1 half times 1 over x plus x squared minus e to the power of x close parentheses space d x end cell row blank equals cell 1 half space ln space open vertical bar x close vertical bar plus 1 third x cubed minus e to the power of x plus c end cell end table

Dengan demikian, integral open parentheses fraction numerator 1 over denominator 2 x end fraction plus x squared minus e to the power of x close parentheses space d x equals 1 half space ln space open vertical bar x close vertical bar plus 1 third x cubed minus e to the power of x plus c 

0

Roboguru

Tentukan nilai dari: c.

Pembahasan Soal:

Rumus integral tak tentu:

integral a x to the power of n space d x equals fraction numerator a over denominator n plus 1 end fraction x to the power of n plus 1 end exponent plus c

integral 1 over x space d x equals ln space open vertical bar x close vertical bar plus c

integral e to the power of x space d x equals e to the power of x plus c

Integral pada soal di atas dapat ditentukan sebagai berikut.

integral open parentheses 5 e to the power of x plus 1 third x cubed minus 4 over x close parentheses space d x equals 5 e to the power of x plus 1 third times 1 fourth x to the power of 4 minus 4 space ln space open vertical bar x close vertical bar plus c equals 5 e to the power of x plus 1 over 12 x to the power of 4 minus 4 space ln space open vertical bar x close vertical bar plus c

Dengan demikian, integral open parentheses 5 e to the power of x plus 1 third x cubed minus 4 over x close parentheses space d x equals 5 e to the power of x plus 1 over 12 x to the power of 4 minus 4 space ln space open vertical bar x close vertical bar plus c 

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Roboguru

Hitung. .

Pembahasan Soal:

Diperoleh intergalnya yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator d x over denominator square root of 2 minus 5 x squared end root end fraction end cell equals cell integral fraction numerator 1 over denominator square root of 5 open parentheses begin display style 2 over 5 end style minus x squared close parentheses end root end fraction d x end cell row blank equals cell integral fraction numerator 1 over denominator square root of 5 times square root of begin display style 2 over 5 end style minus x squared end root end fraction d x end cell row blank equals cell fraction numerator 1 over denominator square root of 5 end fraction times integral fraction numerator 1 over denominator square root of begin display style 2 over 5 end style minus x squared end root end fraction d x end cell row blank equals cell fraction numerator 1 over denominator square root of 5 end fraction times fraction numerator square root of 5 over denominator square root of 5 end fraction times integral fraction numerator 1 over denominator square root of begin display style 2 over 5 end style minus x squared end root end fraction d x end cell row blank equals cell fraction numerator square root of 5 over denominator 5 end fraction times integral fraction numerator 1 over denominator square root of begin display style 2 over 5 end style minus x squared end root end fraction d x end cell end table

Ingatlah bahwa:

integral fraction numerator 1 over denominator a squared minus x squared end fraction d x equals arcsin times x over a

Kemudian diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator square root of 5 over denominator 5 end fraction integral fraction numerator 1 over denominator square root of begin display style 2 over 5 end style minus x squared end root end fraction d x end cell equals cell fraction numerator square root of 5 over denominator 5 end fraction times arcsin times fraction numerator x over denominator square root of begin display style 2 over 5 end style end root end fraction plus C end cell row blank equals cell fraction numerator square root of 5 over denominator 5 end fraction times arcsin times fraction numerator x over denominator begin display style fraction numerator square root of 2 over denominator square root of 5 end fraction end style end fraction plus C end cell row blank equals cell fraction numerator square root of 5 over denominator 5 end fraction times arcsin times x times fraction numerator square root of 5 over denominator square root of 2 end fraction plus C end cell row blank equals cell fraction numerator square root of 5 over denominator 5 end fraction times arcsin times fraction numerator x square root of 5 over denominator square root of 2 end fraction times fraction numerator square root of 2 over denominator square root of 2 end fraction plus C end cell row blank equals cell fraction numerator square root of 5 space arcsin space begin display style fraction numerator straight x square root of 10 over denominator 2 end fraction end style over denominator 5 end fraction plus C end cell end table

Maka, hasil integral dari integral fraction numerator d x over denominator square root of 2 minus 5 x squared end root end fraction adalah fraction numerator square root of 5 space arcsin space begin display style fraction numerator x square root of 10 over denominator 2 end fraction end style over denominator 5 end fraction plus C.

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Roboguru

Hitung. .

Pembahasan Soal:

Diperoleh intergalnya yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator d x over denominator 4 x square root of x squared minus 16 end root end fraction end cell equals cell 1 fourth integral fraction numerator 1 over denominator x square root of x squared minus 16 end root end fraction d x end cell row blank equals cell 1 fourth integral fraction numerator 1 over denominator x square root of x squared minus 4 squared end root end fraction d x end cell end table

Ingatlah bahwa:

integral fraction numerator 1 over denominator x square root of x squared minus a squared end root end fraction d x equals 1 over a times asec open parentheses fraction numerator open vertical bar x close vertical bar over denominator a end fraction close parentheses

Kemudian diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell 1 fourth integral fraction numerator 1 over denominator x square root of x squared minus 4 squared end root end fraction d x end cell equals cell 1 fourth times 1 fourth times asec open parentheses fraction numerator open vertical bar straight x close vertical bar over denominator 4 end fraction close parentheses plus straight C end cell row blank equals cell 1 over 16 times asec open parentheses fraction numerator open vertical bar straight x close vertical bar over denominator 4 end fraction close parentheses plus straight C end cell row blank equals cell fraction numerator asec open parentheses begin display style fraction numerator open vertical bar straight x close vertical bar over denominator 4 end fraction end style close parentheses over denominator 16 end fraction plus straight C end cell end table

Maka, hasil integral dari integral fraction numerator d x over denominator 4 x square root of x squared minus 16 end root end fraction adalah fraction numerator asec open parentheses begin display style fraction numerator open vertical bar x close vertical bar over denominator 4 end fraction end style close parentheses over denominator 16 end fraction plus C.

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Roboguru

Carilah !

Pembahasan Soal:

Dengan menggunakan sifat integral, maka diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator 3 over denominator x squared minus 1 end fraction d x end cell equals cell 3 times open parentheses integral fraction numerator 1 over denominator x squared minus 1 end fraction d x close parentheses end cell row blank equals cell 3 times open parentheses integral fraction numerator 1 over denominator negative left parenthesis negative x squared plus 1 right parenthesis end fraction d x close parentheses end cell row blank equals cell 3 times open parentheses negative integral fraction numerator 1 over denominator negative x squared plus 1 end fraction d x close parentheses end cell row blank equals cell 3 times open parentheses negative open parentheses fraction numerator ln space open vertical bar x plus 1 close vertical bar over denominator 2 end fraction close parentheses minus fraction numerator ln space open vertical bar x minus 1 close vertical bar over denominator 2 end fraction close parentheses plus C end cell row cell integral fraction numerator 3 over denominator x squared minus 1 end fraction d x end cell equals cell negative 3 open parentheses 1 half ln space open vertical bar x plus 1 close vertical bar minus 1 half ln space open vertical bar x minus 1 close vertical bar close parentheses plus C end cell end table 

Dengan demikian, nilai dari integral fraction numerator 3 over denominator x squared minus 1 end fraction d x adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 3 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 1 half ln space open vertical bar x plus 1 close vertical bar minus 1 half ln space open vertical bar x minus 1 close vertical bar close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank C end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank. end table 

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