Reverse an arctangent chain and use a principal sine substitution

(i) Find $\displaystyle\int\dfrac{e^{\tan^{-1}2x}}{1+4x^2}\,dx$.2 marks

(ii) Given that $-\dfrac\pi2<\theta<\dfrac\pi2$, use the substitution $x=\sin\theta$ to find $\displaystyle\int\dfrac{x^2}{\sqrt{1-x^2}}\,dx$.6 marks