Pertanyaan

∫ 6 x ( 6 x + 1 ) 5 d x = …

$\int 6 x (6 x + 1)^{5} d x = \dots$

Ikuti Tryout SNBT & Menangkan E-Wallet 100rb

Habis dalam

Klaim

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

hasil dari adalah

hasil dari integral 6 x open parentheses 6 x plus 1 close parentheses to the power of 5 space straight d x

adalah

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 over 42 open parentheses 6 x plus 1 close parentheses to the power of 7 minus 1 over 36 open parentheses 6 x plus 1 close parentheses to the power of 6 plus C. end cell end table

Pembahasan

Ingat kembali sifat integral berikut: Misalkan: Perhatikan perhitungan berikut ini! Note : baris ke- di atas bukan hasil dari nyoret loh yah. Sehingga, hasil dari adalah Dengan demikian, hasil dari adalah

Ingat kembali sifat integral berikut:

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

Misalkan:

$begin mathsize 14px style u equals 6 x plus 1 left right double arrow x equals fraction numerator u minus 1 over denominator 6 end fraction end style$

Perhatikan perhitungan berikut ini!

$table attributes columnalign right center left columnspacing 0px end attributes row u equals cell 6 x plus 1 end cell row cell fraction numerator straight d u over denominator straight d x end fraction end cell equals 6 row cell integral open parentheses fraction numerator straight d u over denominator straight d x end fraction close parentheses straight d x end cell equals cell integral 6 space straight d x end cell row cell integral straight d u end cell equals cell integral 6 space straight d x end cell end table$

Note : baris ke- di atas bukan hasil dari nyoret straight d x loh yah.

Sehingga, hasil dari integral 6 x open parentheses 6 x plus 1 close parentheses to the power of 5 space straight d x adalah

$table attributes columnalign right center left columnspacing 0px end attributes row cell integral 6 x left parenthesis 6 x plus 1 right parenthesis to the power of 5 space d x end cell equals cell integral x left parenthesis 6 x plus 1 right parenthesis to the power of 5 times 6 space straight d x end cell row blank equals cell integral open parentheses fraction numerator u minus 1 over denominator 6 end fraction close parentheses times u to the power of 5 straight d u end cell row blank equals cell 1 over 6 integral open parentheses u minus 1 close parentheses times u to the power of 5 space straight d u end cell row blank equals cell 1 over 6 integral open parentheses u to the power of 6 minus u to the power of 5 close parentheses space straight d u end cell row blank equals cell 1 over 6 open parentheses 1 over 7 u to the power of 7 minus 1 over 6 u to the power of 6 plus C close parentheses end cell row blank equals cell 1 over 42 u to the power of 7 minus 1 over 36 u to the power of 6 plus C end cell row cell integral 6 x left parenthesis 6 x plus 1 right parenthesis to the power of 5 space d x end cell equals cell 1 over 42 open parentheses 6 x plus 1 close parentheses to the power of 7 minus 1 over 36 open parentheses 6 x plus 1 close parentheses to the power of 6 plus C end cell end table$

Dengan demikian, hasil dari integral 6 x open parentheses 6 x plus 1 close parentheses to the power of 5 space straight d x adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 over 42 open parentheses 6 x plus 1 close parentheses to the power of 7 minus 1 over 36 open parentheses 6 x plus 1 close parentheses to the power of 6 plus C. end cell end table