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Hasil dari integral open parentheses 3 x squared minus 4 close parentheses open parentheses x plus 2 close parentheses straight d x equals horizontal ellipsis

  1. 1 fourth x to the power of 4 plus 2 x cubed minus 3 x squared minus 8 x plus c

  2. 3 over 4 x to the power of 4 plus 2 x cubed minus 2 x squared minus 8 x plus c

  3. 3 over 4 x to the power of 4 plus 2 x cubed plus 2 x squared minus 8 x plus c

  4. 3 x to the power of 4 plus 2 x cubed minus 3 x squared minus 8 x plus c

  5. 3 x to the power of 4 plus 4 x cubed minus 2 x squared minus 8 x plus c

Pembahasan Soal:

Ingatlah bahwa

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dan

begin mathsize 14px style integral k space d x equals k x plus c end style.

Kemudian perhatikan bahwa

open parentheses 3 x squared minus 4 close parentheses open parentheses x plus 2 close parentheses equals 3 x cubed plus 6 x squared minus 4 x minus 8

Akibatnya

table attributes columnalign right center left columnspacing 0px end attributes row cell integral open parentheses 3 x squared minus 4 close parentheses open parentheses x plus 2 close parentheses d x end cell equals cell integral open parentheses 3 x cubed plus 6 x squared minus 4 x minus 8 close parentheses d x end cell row blank equals cell fraction numerator 3 over denominator 3 plus 1 end fraction x to the power of 3 plus 1 end exponent plus fraction numerator 6 over denominator 2 plus 1 end fraction x to the power of 2 plus 1 end exponent end cell row blank blank cell negative fraction numerator 4 over denominator 1 plus 1 end fraction x to the power of 1 plus 1 end exponent minus 8 x plus c end cell row blank equals cell 3 over 4 x to the power of 4 plus 2 x cubed minus 2 x squared minus 8 x plus c end cell end table

Jadi, jawaban yang tepat adalah B.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Acfreelance

Terakhir diupdate 03 Mei 2021

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Pertanyaan yang serupa

Selesaikanlah integral berikut! f.

Pembahasan Soal:

Perhatikan perhitungan berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell integral open parentheses 2 x minus 3 over x close parentheses squared space straight d x end cell equals cell integral open parentheses 2 x minus 3 x to the power of negative 1 end exponent close parentheses squared space straight d x end cell row blank equals cell integral 4 x squared minus 2 times 2 x times 3 x to the power of negative 1 end exponent plus 9 x to the power of negative 2 end exponent space straight d x end cell row blank equals cell integral 4 x squared minus 12 plus 9 x to the power of negative 2 end exponent space straight d x end cell row blank equals cell 4 over 3 x cubed minus 12 x plus fraction numerator 9 over denominator negative 1 end fraction x to the power of negative 1 end exponent plus C end cell row blank equals cell 4 over 3 x cubed minus 12 x minus 9 x to the power of negative 1 end exponent plus C end cell row blank equals cell 4 over 3 x cubed minus 12 x minus 9 over x plus C end cell end table      

Jadi, Error converting from MathML to accessible text..

Roboguru

Hasil dari  adalah ....

Pembahasan Soal:

Ingat kembali bahwa 

undefined 

Maka didapat 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral 5 x blank squared root index 6 of x to the power of 7 end root blank d x end cell equals cell integral 5 x blank to the power of 19 over 6 end exponent blank d x end cell row blank equals cell fraction numerator 5 over denominator 19 over 6 plus 1 end fraction x to the power of 19 over 6 plus 1 end exponent plus C end cell row blank equals cell fraction numerator 5 over denominator 25 over 6 end fraction x to the power of 25 over 6 end exponent plus C end cell row blank equals cell 5 times 6 over 25 x to the power of 25 over 6 end exponent plus C end cell row blank equals cell 6 over 5 x to the power of 25 over 6 end exponent plus C end cell row blank equals cell 6 over 5 x to the power of 4 root index 6 of x plus C end cell end table end style  

Jadi, jawaban yang tepat adalah C.

Roboguru

Hasil dari  adalah ....

Pembahasan Soal:

Misalkan:

Error converting from MathML to accessible text.  

Dengan demikian:

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral left parenthesis x squared plus 2 right parenthesis square root of x cubed plus 6 x plus 1 end root d x end cell equals cell integral 1 third u to the power of 1 half end exponent d u end cell row blank equals cell 1 third cross times fraction numerator u to the power of begin display style 3 over 2 end style end exponent over denominator begin display style bevelled 3 over 2 end style end fraction plus C end cell row blank equals cell 2 u to the power of 3 over 2 end exponent plus C end cell row blank equals cell 2 left parenthesis x cubed plus 6 x plus 1 right parenthesis to the power of 3 over 2 end exponent plus C end cell row blank equals cell 2 open parentheses x cubed plus 6 x plus 1 close parentheses square root of x cubed plus 6 x plus 1 end root plus C end cell end table end style 

Jadi, jawaban yang tepat adalah A

Roboguru

Selesaikanlah integral berikut! a.

Pembahasan Soal:

Perhatikan perhitungan berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell integral x open parentheses square root of x minus 1 close parentheses space straight d x end cell equals cell space integral x open parentheses x to the power of 1 half end exponent minus 1 close parentheses space straight d x end cell row blank equals cell space integral x to the power of 3 over 2 end exponent minus x space straight d x end cell row blank equals cell fraction numerator 1 over denominator begin display style 5 over 2 end style end fraction x to the power of 5 over 2 end exponent minus 1 half x squared plus C end cell row blank equals cell 2 over 5 x to the power of 5 over 2 end exponent minus 1 half x squared plus C end cell row blank equals cell 2 over 5 x squared square root of x minus 1 half x squared plus C end cell end table 

Jadi, Error converting from MathML to accessible text..

Roboguru

Hasil dari  adalah ....

Pembahasan Soal:

Perhatikan perhitungan berikut ini! 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator left parenthesis x minus 1 right parenthesis squared left parenthesis x to the power of 2 end exponent minus 2 right parenthesis over denominator x minus square root of 2 end fraction space d x end cell equals cell integral fraction numerator left parenthesis x minus 1 right parenthesis squared left parenthesis x plus square root of 2 right parenthesis left parenthesis x minus square root of 2 right parenthesis over denominator x minus square root of 2 end fraction space d x end cell row blank equals cell integral left parenthesis x minus 1 right parenthesis squared left parenthesis x plus square root of 2 right parenthesis space d x end cell row blank equals cell integral left parenthesis x squared minus 2 x plus 1 right parenthesis left parenthesis x plus square root of 2 right parenthesis space d x end cell row blank equals cell integral left parenthesis x cubed plus square root of 2 x squared minus 2 x squared minus 2 square root of 2 x plus x plus square root of 2 right parenthesis space d x end cell row blank equals cell integral left parenthesis x cubed plus left parenthesis square root of 2 minus 2 right parenthesis x squared minus open parentheses 2 square root of 2 plus 1 close parentheses x plus square root of 2 right parenthesis space d x end cell row blank equals cell open parentheses fraction numerator 1 over denominator 3 plus 1 end fraction x to the power of 3 plus 1 end exponent plus C subscript 1 close parentheses plus left parenthesis square root of 2 minus 2 right parenthesis open parentheses fraction numerator 1 over denominator 2 plus 1 end fraction x to the power of 2 plus 1 end exponent plus C subscript 2 close parentheses minus open parentheses 2 square root of 2 plus 1 close parentheses open parentheses fraction numerator 1 over denominator 1 plus 1 end fraction x to the power of 1 plus 1 end exponent plus C subscript 3 close parentheses plus square root of 2 open parentheses x plus C subscript 4 close parentheses end cell row blank equals cell 1 fourth x to the power of 4 plus fraction numerator square root of 2 minus 1 over denominator 3 end fraction x cubed minus fraction numerator 2 square root of 2 plus 1 over denominator 2 end fraction x squared plus square root of 2 x plus C subscript 1 plus left parenthesis square root of 2 minus 2 right parenthesis C subscript 2 minus open parentheses 2 square root of 2 plus 1 close parentheses C subscript 3 plus square root of 2 C subscript 4 end cell end table end style

Jika dimisalkan begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell C subscript 1 plus left parenthesis square root of 2 minus 2 right parenthesis C subscript 2 minus left parenthesis 2 square root of 2 plus 1 right parenthesis C subscript 3 plus square root of 2 C subscript 4 end cell 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 C end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table end style maka

size 14px 1 over size 14px 4 size 14px x to the power of size 14px 4 size 14px plus fraction numerator square root of size 14px 2 size 14px minus size 14px 1 over denominator size 14px 3 end fraction size 14px x to the power of size 14px 3 size 14px minus fraction numerator size 14px 2 square root of size 14px 2 size 14px plus size 14px 1 over denominator size 14px 2 end fraction size 14px x to the power of size 14px 2 size 14px plus square root of size 14px 2 size 14px x size 14px plus size 14px C subscript size 14px 1 size 14px plus size 14px left parenthesis square root of size 14px 2 size 14px minus size 14px 2 size 14px right parenthesis size 14px C subscript size 14px 2 size 14px minus begin mathsize 14px style left parenthesis 2 square root of 2 plus 1 right parenthesis end style size 14px C subscript size 14px 3 size 14px plus square root of size 14px 2 size 14px C subscript size 14px 4 size 14px equals size 14px 1 over size 14px 4 size 14px x to the power of size 14px 4 size 14px plus fraction numerator square root of size 14px 2 size 14px minus size 14px 1 over denominator size 14px 3 end fraction size 14px x to the power of size 14px 3 size 14px minus fraction numerator size 14px 2 square root of size 14px 2 size 14px plus size 14px 1 over denominator size 14px 2 end fraction size 14px x to the power of size 14px 2 size 14px plus square root of size 14px 2 size 14px x size 14px plus size 14px C 

Jadi, jawaban yang tepat adalah A.

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