AM-1963

Integrating f(ax + b)

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

Given that

\dfrac{10x-7}{x^2(3x-2)} = -\dfrac{13}{4x} + \dfrac{7}{2x^2} + \dfrac{39}{4(3x-2)}

, find

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

.

$-\dfrac{13}{4}\ln|x| - \dfrac{7}{2x} + \dfrac{13}{4}\ln|3x-2| + C$
$-\dfrac{13}{4}\ln|x| + \dfrac{7}{2x} + \dfrac{13}{4}\ln|3x-2| + C$
$-\dfrac{13}{4}\ln|x| - \dfrac{7}{2x} + \dfrac{39}{4}\ln|3x-2| + C$
$-\dfrac{13}{4x} - \dfrac{7}{2x} + \dfrac{13}{4}\ln|3x-2| + C$

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