Find $\displaystyle\int{\frac{1}{\left( ax-b \right)\left( ax+3b \right)}}\,\mathrm{d}x$, where $a$

Question

Find $\displaystyle\int{\frac{1}{\left( ax-b \right)\left( ax+3b \right)}}\,\mathrm{d}x$, where $a$ and $b$ are positive constants. [3] Use the substitution $u=\sqrt{{{x}^{3}}}$ to find the exact value of $\displaystyle\int_{0}^{\sqrt[3]{3}}{\frac{\sqrt{x}}{1+{{x}^{3}}}}\,\mathrm{d}x$. [3]

Accepted Answer

(a) $\frac1{4ab}\ln\left|\frac{ax-b}{ax+3b}\right|+C$; (b) $\frac{2\pi}{9}$

2022 DHS J2 MYE P1 Q2

2022 DHS J2 MYE P1 Q2

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