Integration by partsEdexcel A-Level Maths: Mind map

Exam questions on Integration by parts

1. Let $I=\int xe^{2x}\,\mathrm{d}x$, to be found by integration by parts.
   Hence find the exact value of $\int_0^1xe^{2x}\,\mathrm{d}x$.2 marks
2. Integration by parts uses $\int u\frac{\mathrm{d}v}{\mathrm{d}x}\,\mathrm{d}x=uv-\int v\frac{\mathrm{d}u}{\mathrm{d}x}\,\mathrm{d}x$.
   Find $\int x^2\ln x\,\mathrm{d}x$ for $x>0$.2 marks
3. In this question, use integration by parts.
   Find $\int x\sin2x\,\mathrm{d}x$.3 marks