Find $\displaystyle \displaystyle\int \frac{x}{\sqrt{16-x^4}} \, \mathrm{d}x$.[2] Find \(\displays

Question

Find $\displaystyle \displaystyle\int \frac{x}{\sqrt{16-x^4}} \, \mathrm{d}x$.[2] Find $\displaystyle \displaystyle\int \frac{x}{2} \sin^{-1} \left( \frac{x^2}{4} \right) \, \mathrm{d}x$.[5]

Accepted Answer

(a) $\frac12\sin^{-1}\left(\frac{x^2}{4}\right)+C$; (b) $\frac{x^2}{4}\sin^{-1}\left(\frac{x^2}{4}\right)+\frac14\sqrt{16-x^4}+C$.

2025 RVHS P1 Q5

2025 RVHS P1 Q5

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