2018 TJC Promo Q5
(b)
Without using a graphing calculator, show that
$\int_{0}^{1}{\frac{{{x}^{3}}}{1+{{x}^{2}}}}\text{ d}x=k\left( 1-\ln 2 \right)$,
where $k$ is a real number to be determined.
[3]
Hence find $\int_{0}^{1}{{{x}^{2}}{{\tan }^{-1}}x}\text{ d}x$, leaving your answer in exact form.
[3]
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