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Pertanyaan

integral fraction numerator open parentheses x plus 1 close parentheses open parentheses x minus 3 close parentheses over denominator square root of x end fraction d x equals horizontal ellipsis

  1. 2 over 5 x squared square root of x minus 4 over 3 x square root of x minus 6 square root of x plus C

  2. 2 over 5 x squared square root of x plus 4 over 3 x square root of x minus 6 square root of x plus C

  3. 2 over 5 x squared square root of x plus 4 over 3 x square root of x plus 6 square root of x plus C

  4. 2 over 5 x squared square root of x minus 4 over 3 x square root of x plus 6 square root of x plus C

  5. 2 over 5 x squared square root of x minus 4 over 3 x square root of x minus 6 square root of x

Pembahasan Soal:

Error converting from MathML to accessible text.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

N. Ayu

Mahasiswa/Alumni Universitas Negeri Padang

Terakhir diupdate 16 Desember 2020

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Pertanyaan yang serupa

Tentukan integral dari ∫x​3x+2​dx=...

Pembahasan Soal:

Cara pengerjaan integral tak tentu adalah integral straight a x to the power of straight n space d x equals fraction numerator a over denominator straight n plus 1 end fraction x to the power of straight n plus 1 end exponent plus C.

Maka:


table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator 3 x plus 2 over denominator square root of x end fraction space d x end cell equals cell space integral left parenthesis 3 x plus 2 right parenthesis times x to the power of negative 1 half end exponent space d x end cell row blank equals cell integral 3 x to the power of 1 half end exponent plus 2 x to the power of negative 1 half end exponent space d x end cell row blank equals cell fraction numerator 3 over denominator begin display style 1 half end style plus 1 end fraction x to the power of 3 over 2 end exponent plus fraction numerator 2 over denominator negative begin display style 1 half end style plus 1 end fraction x to the power of 1 half end exponent plus C end cell row blank equals cell 2 x to the power of 3 over 2 end exponent plus 4 x to the power of 1 half end exponent plus C end cell row blank equals cell 2 x square root of x plus 4 square root of x plus C end cell end table


Jadi table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator 3 x plus 2 over denominator square root of x end fraction space d x end cell equals cell 2 x square root of x plus 4 square root of x plus C end cell end table.

0

Roboguru

∫xx2−x​​dx=...

Pembahasan Soal:

Ingat, 

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 comma space space space n not equal to negative 1 

Ktia sederhanakan terlebih dahulu integrannya. Ingat 

a to the power of n over a to the power of m equals a to the power of n minus m end exponent space space space space space comma space space space square root of a equals a to the power of 1 half end exponent 

maka

 integral fraction numerator x squared minus square root of x over denominator x end fraction space d x equals integral x minus x to the power of negative begin inline style 1 half end style end exponent space d x space space space space space space space space space space space space space space space space space space space space space space space equals 1 half x squared minus fraction numerator 1 over denominator 1 half end fraction x to the power of begin inline style 1 half end style end exponent plus C space space space space space space space space space space space space space space space space space space space space space space space equals 1 half x squared minus 2 square root of x plus C

Jadi, jawaban yang tepat adalah C.

0

Roboguru

Hasil dari ∫2x−5​4​dx adalah ...

Pembahasan Soal:

Ingat materi integral tak tentu pada pecahan dan turunan.

Misalkan 

table attributes columnalign right center left columnspacing 0px end attributes row u equals cell 2 x minus 5 end cell row cell fraction numerator straight d u over denominator straight d x end fraction end cell equals 2 row cell straight d u end cell equals cell 2 blank straight d x end cell row cell fraction numerator straight d u over denominator 2 end fraction end cell equals cell straight d x end cell end table

sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator 4 over denominator square root of 2 x minus 5 end root end fraction straight d x end cell equals cell integral fraction numerator 4 over denominator square root of u end fraction fraction numerator straight d u over denominator 2 end fraction end cell row blank equals cell integral fraction numerator 2 over denominator square root of u end fraction blank straight d u end cell row blank equals cell integral 2 u to the power of negative 1 half end exponent blank straight d u end cell row blank equals cell 2 integral u to the power of negative 1 half end exponent blank straight d u end cell row blank equals cell 2 times fraction numerator 1 over denominator negative 1 half plus 1 end fraction u to the power of negative 1 half plus 1 end exponent plus C end cell row blank equals cell 2 times fraction numerator 1 over denominator negative 1 half plus 2 over 2 end fraction u to the power of negative 1 half plus 2 over 2 end exponent plus C end cell row blank equals cell 2 times fraction numerator 1 over denominator 1 half end fraction u to the power of 1 half end exponent plus C end cell row blank equals cell 2 times 2 times u to the power of 1 half end exponent plus C end cell row blank equals cell 4 u to the power of 1 half end exponent plus C end cell row blank equals cell 4 left parenthesis 2 x minus 5 right parenthesis to the power of 1 half end exponent plus C end cell row blank equals cell 4 square root of 2 x minus 5 end root plus C end cell end table

Oleh karena itu, jawaban yang benar adalah E.

1

Roboguru

Selesaikanlah integral berikut! e. ∫x2x2−3​dx

Pembahasan Soal:

Perhatikan perhitungan berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator x squared minus 3 over denominator x squared end fraction space straight d x end cell equals cell integral x to the power of negative 2 end exponent open parentheses x squared minus 3 close parentheses space straight d x end cell row blank equals cell integral 1 minus 3 x to the power of negative 2 end exponent space straight d x end cell row blank equals cell x minus fraction numerator 3 over denominator negative 1 end fraction x to the power of negative 1 end exponent plus C end cell row blank equals cell x plus 3 x to the power of negative 1 end exponent plus C end cell row blank equals cell x plus 3 over x plus C end cell end table     

Jadi, table attributes columnalign right center left columnspacing 0px end attributes row blank blank integral end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator x squared minus 3 over denominator x squared end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight d end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x 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 cell 3 over x 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.

1

Roboguru

∫(x3+xx4−1​)2dx=...

Pembahasan Soal:

Untuk menentukan turunan dari bentuk di atas, maka kita dapat menyederhanakan bentuk tersebut:

table attributes columnalign right center left columnspacing 0px end attributes row cell integral open parentheses fraction numerator x to the power of 4 minus 1 over denominator x cubed plus x end fraction close parentheses squared d x end cell equals cell integral open parentheses fraction numerator x to the power of 4 minus 1 over denominator x open parentheses x squared plus 1 close parentheses end fraction close parentheses squared d x end cell row blank equals cell integral open parentheses fraction numerator open parentheses x squared minus 1 close parentheses open parentheses x squared plus 1 close parentheses over denominator x open parentheses x squared plus 1 close parentheses end fraction close parentheses squared d x end cell row blank equals cell integral open parentheses fraction numerator open parentheses x squared minus 1 close parentheses over denominator x end fraction close parentheses squared d x end cell row blank equals cell integral open parentheses x squared over x minus 1 over x close parentheses squared d x end cell row blank equals cell integral open parentheses x minus 1 over x close parentheses squared d x end cell row blank equals cell integral x squared minus 2 x times 1 over x plus open parentheses 1 over x close parentheses squared space d x end cell row blank equals cell integral x squared minus 2 plus x to the power of negative 2 end exponent space d x end cell row blank equals cell 1 third x cubed minus 2 x minus x to the power of negative 1 end exponent plus c end cell row blank equals cell 1 third x cubed minus 2 x minus 1 over x plus c end cell row blank equals blank end table

Jadi, hasil dari Error converting from MathML to accessible text. adalah 1 third x cubed minus 2 x minus 1 over x plus c

0

Roboguru

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