(Solved): Question 6 - 10 marks You should be able to answer this question after studyi ...

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Question 6 - 10 marks You should be able to answer this question after studying Unit 8. (a) Use integration by substitution to find the indefinite integral \[ \int \frac{x^{5}-x^{2}}{\left(x^{3}-1\right)^{1 / 3}} d x \] (Hint: it may help to factorise the numerator.) (b) Use integration by parts twice to find the indefinite integral \[ \int\left(y^{2}+1\right) e^{-y} \mathrm{~d} y \]