Find $\int x\left[ (1-3x^2)^5 + \mathrm{e}^{x^2+1} \right] \mathrm{d}x$.[3] Find \(\frac{\mathrm{d

Question

Find $\int x\left[ (1-3x^2)^5 + \mathrm{e}^{x^2+1} \right] \mathrm{d}x$.[3] Find $\frac{\mathrm{d}}{\mathrm{d}x}\cos^{-1}(x^2)$. Hence, or otherwise, find the exact value of $\int_{0}^{\frac{1}{\sqrt{2}}} \frac{x}{\sqrt{(1-x^4)}} \mathrm{d}x$.[3]

Accepted Answer

(b) $-\frac1{36}(1-3x^2)^6+\frac12\mathrm{e}^{x^2+1}+c$ (c) $\frac{\pi}{12}$

2016 DHS C1BT Q2

2016 DHS C1BT Q2

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