Indefinite integrationEdexcel International A Level Maths: Mind map

Exam questions on Indefinite integration

1. Let $g(x)=6x^2-4x+5$.
   Find $\int\left(g(x)+\frac{4}{x^3}\right)\mathrm{d}x$.2 marks
2. A function is defined by $f(x)=4\sqrt{x}-\dfrac{6}{x^3}$ for $x>0$.
   Find $\int x^3f(x)\,\mathrm{d}x$.2 marks
3. The function $f$ is defined by $f(x)=\dfrac{(2x+1)^2}{\sqrt{x}}$ for $x>0$.
   Show that $f(x)=4x^{\frac32}+4x^{\frac12}+x^{-\frac12}$.3 marks