Pertanyaan

∫ 3 6 x − 5 4 d x = ...

$\int \frac{4}{3 6 x - 5} d x = ...$

M. Rochmat

Master Teacher

Jawaban terverifikasi

Jawaban

hasil dari ∫ 3 6 x − 5 4 d x adalah ( 6 x − 5 ) 3 2 + c .

hasil dari

\int \frac{4}{3 6 x - 5} d x

adalah

(6 x - 5)^{\frac{2}{3}} + c

Pembahasan

∫ 3 6 x − 5 4 d x = ∫ 4 ( 6 x − 5 ) − 3 1 d x Misalkan : Sehingga, Jadi, hasil dari ∫ 3 6 x − 5 4 d x adalah ( 6 x − 5 ) 3 2 + c .

$\int \frac{4}{3 6 x - 5} d x = \int 4 (6 x - 5)^{- \frac{1}{3}} d x$

Misalkan :

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row u equals cell 6 x minus 5 end cell row cell fraction numerator d u over denominator d x end fraction end cell equals cell 6 left right double arrow straight d x equals fraction numerator straight d u over denominator 6 end fraction end cell end table end style$

Sehingga,

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral 4 u to the power of negative 1 third end exponent fraction numerator straight d u over denominator 6 end fraction end cell equals cell 2 over 3 integral u to the power of negative 1 third end exponent straight d u end cell row blank equals cell 2 over 3 cross times 3 over 2 cross times u to the power of 2 over 3 end exponent plus straight c end cell row blank equals cell u to the power of 2 over 3 end exponent plus straight c end cell row blank equals cell open parentheses 6 straight x minus 5 close parentheses to the power of 2 over 3 end exponent plus straight c end cell end table end style$

Jadi, hasil dari $\int \frac{4}{3 6 x - 5} d x$ adalah $(6 x - 5)^{\frac{2}{3}} + c$ .