Pertanyaan

∫ x 3 ( x + 1 ) 3 d x

$\int x^{3} (x + 1)^{3} d x$

S. Difhayanti

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. Dr. Hamka

Jawaban terverifikasi

Jawaban

adalah .

integral x cubed open parentheses x plus 1 close parentheses cubed space d x

adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight x to the power of 7 over 7 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight x to the power of 6 over 2 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 3 straight x to the power of 5 over denominator 5 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight x to the power of 4 over 4 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight C end table$ .

Pembahasan

Dengan menggunakan konsep integral tak tentu, rumusnya yaitu : Maka, Jadi, adalah .

Dengan menggunakan konsep integral tak tentu, rumusnya yaitu :

$integral a x to the power of n d x equals fraction numerator a over denominator n plus 1 end fraction x to the power of n plus 1 end exponent plus C comma space untuk space n not equal to negative 1$

Maka,

$table attributes columnalign right center left columnspacing 0px end attributes row cell integral x cubed open parentheses x plus 1 close parentheses cubed space d x end cell equals cell integral x cubed open parentheses x cubed plus 3 x squared plus 3 x plus 1 close parentheses space d x end cell row blank equals cell integral open parentheses x to the power of 6 plus 3 x to the power of 5 plus 3 x to the power of 4 plus x cubed close parentheses space d x end cell row blank equals cell integral x to the power of 6 space d x plus 3 integral x to the power of 5 space d x plus 3 integral x to the power of 4 space d x plus integral x cubed space d x end cell row blank equals cell fraction numerator x to the power of 6 plus 1 end exponent over denominator 6 plus 1 end fraction plus fraction numerator 3 x to the power of 5 plus 1 end exponent over denominator 5 plus 1 end fraction plus fraction numerator 3 x to the power of 4 plus 1 end exponent over denominator 4 plus 1 end fraction plus fraction numerator x to the power of 3 plus 1 end exponent over denominator 3 plus 1 end fraction plus straight C end cell row blank equals cell straight x to the power of 7 over 7 plus fraction numerator 3 straight x to the power of 6 over denominator 6 end fraction plus fraction numerator 3 straight x to the power of 5 over denominator 5 end fraction plus straight x to the power of 4 over 4 plus straight C end cell row blank equals cell straight x to the power of 7 over 7 plus straight x to the power of 6 over 2 plus fraction numerator 3 straight x to the power of 5 over denominator 5 end fraction plus straight x to the power of 4 over 4 plus straight C end cell end table$

Jadi, integral x cubed open parentheses x plus 1 close parentheses cubed space d x adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight x to the power of 7 over 7 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight x to the power of 6 over 2 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 3 straight x to the power of 5 over denominator 5 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight x to the power of 4 over 4 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight C end table$ .