Find $\displaystyle\int (4x-1)^5 - \frac{1}{3-2x} \, \mathrm{d}x$.[3] Differentiate \(e^{(3x^2-4)}

Question

Find $\displaystyle\int (4x-1)^5 - \frac{1}{3-2x} \, \mathrm{d}x$.[3] Differentiate $e^{(3x^2-4)}$ with respect to $x$. Hence, find $\displaystyle\int xe^{(3x^2-4)} \, \mathrm{d}x$.[4]

Accepted Answer

(a)$\frac{1}{24}(4x-1)^6+\frac{1}{2}\ln (3-2x)+c$ (b)$6xe^{(3x^2-4)}$,$\frac{1}{6}e^{(3x^2-4)}+c$

2024 CJC H1 Q2

2024 CJC H1 Q2