Integration by substitutionEdexcel International A Level Maths: Mind map

Exam questions on Integration by substitution

1. Let $I=\int 2x(x^2+3)^4\,dx$. Use the substitution $u=x^2+3$.
   Hence find the exact value of $\int_0^1 2x(x^2+3)^4\,dx$.2 marks
2. Let $I=\int x\sqrt{x-2}\,dx$. Use the substitution $u=x-2$.
   Hence find the exact value of $\int_2^6x\sqrt{x-2}\,dx$.2 marks
3. Let $I=\int_0^4\frac{x}{\sqrt{2x+1}}\,dx$.
   Using the substitution $u=2x+1$, show that $I=\frac14\int_1^9\left(u^{1/2}-u^{-1/2}\right)du$.3 marks