AM-2233

Integrating f(ax + b)

A Math · Secondary 4 · Hard · Integrating f(ax + b)

Given that

\dfrac{10x-7}{x^2(3x-2)}=-\dfrac{11}{12x}+\dfrac{7}{2x^2}+\dfrac{11}{4(3x-2)}

, find

\displaystyle\int \dfrac{10x-7}{x^2(3x-2)}\,dx

.

$-\dfrac{11}{12}\ln|x|-\dfrac{7}{2x}+\dfrac{11}{12}\ln|3x-2|+C$
$-\dfrac{11}{12}\ln|x|+\dfrac{7}{2x}+\dfrac{11}{12}\ln|3x-2|+C$
$-\dfrac{11}{12}\ln|x|-\dfrac{7}{2x}+\dfrac{11}{4}\ln|3x-2|+C$
$-\dfrac{11}{4}\ln|x|-\dfrac{7}{2x}+\dfrac{11}{12}\ln|3x-2|+C$

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