Integration by substitutionEdexcel A-Level Maths: Mind map

Exam questions on Integration by substitution

1. Let $I=\int x\left(x^2+3\right)^4\,\mathrm{d}x$.
   Hence find the exact value of $\int_0^1x\left(x^2+3\right)^4\,\mathrm{d}x$.2 marks
2. Let $N=\int_0^{\ln2}\frac{e^{x}}{1+e^{x}}\,\mathrm{d}x$, to be found using the substitution $u=1+e^x$.
   Hence find the exact value of $N$.2 marks
3. In this question, use integration by substitution with the substitution given in each part.
   Use $u=1-x^2$ to find $\int\frac{x}{\sqrt{1-x^2}}\,\mathrm{d}x$ for $|x|<1$.3 marks