Find the indefinite integral ∫(x^2)*(e^x) dx (Edexcel C4 June 2013 Question 1)

This is an example question where you integrate by parts twice. When answering a question like this it is helpful to memorise general integration formula, so you can quickly and confidently tackle questions like this. For this question ∫(x^2)(e^x) dx = ∫udv =uv- ∫vdu where [u=x^2] and [dv= (e^x)dx]; differentiate both sides of the equation [u=x^2] to get [du=2x dx] and integrate both sides of the the equation [dv= (e^x)dx] to get [v=e^x]. Substituting these terms into the general formula, you get (x^2)(e^x)- ∫ (e^x)(2x)dx. Now, integrate ∫ ((e^x)(2x) dx by parts using the same process. The overall expression now simplifies to (x^2)(e^x)-[2x *(e^x)- 2 ∫ (e^x) dx]. This then can be solved to get (x^2)(e^x)-2[x(e^x)-e^x]+c. (Do not forget to add the constant).