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Hasil dari ∫x​(x​+2)3​dx=....

Pertanyaan

Hasil dari integral fraction numerator open parentheses square root of x plus 2 close parentheses cubed over denominator square root of x end fraction straight d x equals.... 

  1. 1 half open parentheses square root of x plus 2 close parentheses to the power of 4 plus C

  2. 1 fourth open parentheses square root of x plus 2 close parentheses to the power of 4 plus C

  3. 1 third open parentheses square root of x plus 2 close parentheses to the power of 4 plus C

  4. 2 over 3 open parentheses square root of x plus 2 close parentheses to the power of 4 plus C

  5. 1 half open parentheses 2 square root of x plus 1 close parentheses to the power of 4 plus C

Pembahasan Soal:

Ingat kembali tentang integral subsitusi.

Misalkan u equals square root of x plus 2 comma space fraction numerator d u over denominator d x end fraction equals fraction numerator 1 over denominator 2 square root of x end fraction, maka 

table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator open parentheses square root of x plus 2 close parentheses cubed over denominator square root of x end fraction straight d x end cell equals cell 2 integral u cubed d u end cell row blank equals cell 2 times 1 fourth u to the power of 4 plus C end cell row blank equals cell 1 half u to the power of 4 plus C end cell row blank equals cell 1 half open parentheses square root of x plus 2 close parentheses to the power of 4 plus C end cell end table

Oleh karena itu, jawaban yang benar adalah A.

 

 

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

Y. Endah

Mahasiswa/Alumni Institut Teknologi Bandung

Terakhir diupdate 07 Oktober 2021

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Pertanyaan yang serupa

Hasil dari  ∫(3x+2)(3x2+4x−1)2dx...

Pembahasan Soal:

begin mathsize 14px style integral open parentheses 3 x plus 2 close parentheses open parentheses 3 x squared plus 4 x minus 1 close parentheses squared d x  misalkan colon space u equals 3 x squared plus 4 x minus 1 fraction numerator d u over denominator d x end fraction equals 6 x plus 4 1 half fraction numerator d u over denominator d x end fraction equals 3 x plus 2 1 half straight d u equals 3 x plus 2 space straight d x  integral open parentheses 3 x plus 2 close parentheses open parentheses 3 x squared plus 4 x minus 1 close parentheses squared d x equals integral 1 half space u squared space straight d u equals 1 half times fraction numerator 1 over denominator 2 plus 1 end fraction u cubed plus straight C equals 1 over 6 u cubed plus straight C equals 1 over 6 left parenthesis 3 x squared plus 4 x minus 1 right parenthesis cubed plus straight C space space end style  

0

Roboguru

Integral dari 5x2(x3−2)7 adalah ...

Pembahasan Soal:

Ingat aturan integral berikut.

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

Pada soal tersebut, penyelesaian integral menggunakan metode integral substitusi.

integral 5 x squared open parentheses x cubed minus 2 close parentheses to the power of 7 text  d end text x

Misal: u equals x cubed minus 2 sehingga diperoleh hubungan berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator text d end text u over denominator text d end text x end fraction end cell equals cell 3 x squared end cell row cell integral open parentheses fraction numerator text d end text u over denominator text d end text x end fraction close parentheses text d end text x end cell equals cell integral 3 x squared space text d end text x end cell row cell integral text d end text u end cell equals cell integral 3 x squared space text d end text x end cell row cell integral fraction numerator 1 over denominator 3 x squared end fraction text d end text u end cell equals cell integral text d end text x end cell end table

Selanjutnya, perhatikan perhitungan berikut ini.

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell integral 5 x squared open parentheses x cubed minus 2 close parentheses to the power of 7 space text d end text x end cell row blank equals cell integral 5 x squared times u to the power of 7 times fraction numerator 1 over denominator 3 x squared end fraction text d end text u end cell row blank equals cell integral 5 over 3 u to the power of 7 space text d end text u end cell row blank equals cell 5 over 3 times 1 over 8 u to the power of 8 plus C end cell row blank equals cell 5 over 24 u to the power of 8 plus C end cell end table

Ingat bahwa u equals x cubed minus 2 sehingga diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell integral 5 x squared open parentheses x cubed minus 2 close parentheses to the power of 7 space text d end text x end cell equals cell 5 over 24 u to the power of 8 plus C end cell row blank equals cell 5 over 24 open parentheses x cubed minus 2 close parentheses to the power of 8 plus C end cell end table

Dengan demikian, Error converting from MathML to accessible text.

0

Roboguru

Hasil

Pembahasan Soal:

M i s a l space u equals square root of x squared minus 4 x plus 5 end root comma space m a k a space d u equals fraction numerator x minus 2 over denominator square root of x squared minus 4 x plus 5 end root end fraction d x comma space S e h i n g g a comma  integral subscript space superscript space fraction numerator 4 x minus 8 over denominator square root of x squared minus 4 x plus 5 end root end fraction space d x equals space integral subscript space superscript space fraction numerator 4 open parentheses x minus 2 close parentheses over denominator square root of x squared minus 4 x plus 5 end root end fraction space d x space  equals 4 integral subscript space superscript space fraction numerator open parentheses x minus 2 close parentheses over denominator square root of x squared minus 4 x plus 5 end root end fraction space d x space  equals 4 integral subscript space superscript space d u space  equals 4 u plus C  equals 4 square root of x squared minus 4 x plus 5 end root plus C

0

Roboguru

Hasil dari ∫x2−3x−5​6x−9​dx adalah ....

Pembahasan Soal:

begin mathsize 14px style Misal colon straight u equals straight x squared minus 3 straight x minus 5  du equals 2 straight x minus 3 space dx  du equals left parenthesis 2 straight x minus 3 right parenthesis dx space  3 space du equals left parenthesis 6 straight x minus 9 right parenthesis dx    integral fraction numerator 6 straight x minus 9 over denominator square root of straight x squared minus 3 straight x minus 5 end root end fraction straight space dx  equals integral fraction numerator 1 over denominator square root of straight u end fraction straight space. straight space 3 space du  equals integral 3 straight u to the power of negative 1 half end exponent du  equals fraction numerator 3 over denominator 1 half end fraction straight u to the power of 1 half end exponent plus straight C  equals 6 square root of straight u plus straight C  equals 6 square root of straight x squared minus 3 straight x minus 5 end root plus straight C end style

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Roboguru

hasildari∫​(3x−2)3x24x​dx=....

Pembahasan Soal:

M i s a l k a n space colon U space equals space 3 x squared space – space 4 x space space space  fraction numerator d U over denominator d x end fraction space equals space 6 x space minus 4 space space space  fraction numerator d U over denominator d x end fraction space equals space 2 space left parenthesis 3 x minus 2 right parenthesis space  fraction numerator d U over denominator 2 end fraction space equals space left parenthesis 3 x space minus 2 right parenthesis space. space d x  integral left parenthesis 3 x minus 2 right parenthesis square root of left parenthesis 3 x squared minus 4 x right parenthesis end root d x equals integral square root of left parenthesis 3 x squared minus 4 x right parenthesis end root left parenthesis 3 x minus 2 right parenthesis d x  equals integral U to the power of 1 half end exponent. fraction numerator d U over denominator 2 end fraction  equals 1 half.2 over 3. U to the power of 3 over 2 end exponent plus C  equals 1 third left parenthesis 3 x squared minus 4 x right parenthesis square root of left parenthesis 3 x squared minus 4 x right parenthesis end root plus C

0

Roboguru

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