Integration by partsEdexcel International A Level Maths: Mind map

Exam questions on Integration by parts

1. Let $I=\int xe^{3x}\,dx$.
   Hence find the exact value of $\int_0^1xe^{3x}\,dx$.2 marks
2. Let $I=\int\ln x\,dx$, for $x>0$.
   The region $R$ is bounded by the curve $y=\ln x$, the $x$-axis and the line $x=e$. Find the area of $R$.2 marks
3. Let $I=\int_0^1x^2e^{x}\,dx$.
   Show that $I=e-2\int_0^1xe^{x}\,dx$.3 marks