Find the exact value of $\displaystyle\int_0^{\frac{\pi}{4}}x\tan^2x\,\mathrm{d}x$.[4] By expressi

Question

Find the exact value of $\displaystyle\int_0^{\frac{\pi}{4}}x\tan^2x\,\mathrm{d}x$.[4] By expressing $\dfrac{16}{(x-2)(x^2+4)}$ in partial fractions, find $\displaystyle\int\dfrac{16}{(x-2)(x^2+4)}\,\mathrm{d}x$.[5]

Accepted Answer

(a) $\dfrac{\pi}{4}-\dfrac{1}{2}\ln2-\dfrac{\pi^2}{32}$ (b) $2\ln\lvert x-2\rvert-\ln\left(x^2+4\right)-2\tan^{-1}\left(\dfrac{x}{2}\right)+c$

2026 NJC Promo Q7

2026 NJC Promo Q7

Solution:

Solution locked