Transform a square-root integral and reverse an exponential chain

(a) Use the substitution $u=\sqrt{x+1}$ to find $\displaystyle\int\dfrac{x^2}{\sqrt{x+1}}\,dx$.4 marks

(b) Find $\displaystyle\int\dfrac{e^{5x}}{(e^{5x}-e)^4}\,dx$.3 marks