NYJC/2021/JC2/Prelim/P1/Q06

(a) Find the exact value of $\int_{-3}^{-1} \frac{|x+2|}{x^2+4 x+5} d x$.

[4]

(b) (i) Write down $\int \frac{\sin (ln x)}{x} d x$, where $x>0$.

[1]

(ii) Hence find $\int x \sin (ln x) d x$.

[4]