9758/2021/P2/Q05

(a) Find $\int \tan ^2 5 x d x$.

[2]

(b) Find $\int_0^b \sin 2 x \sin 3 x d x$

[3]

(c) Find $\int_{-a}^b \frac{1}{x \ln x} \mathrm{~d} x$, where $1<a<b$.

[3]

(d) Use the substitution $u=1+\mathrm{e}^{2 x}$ to find $\int \frac{\mathrm{e}^{2 x}}{\left(1+\mathrm{e}^{2 x}\right)^3} d x$.

[3]