A-Level Maths: H5-32 Further Integration: Integrate x*(x+1)^5 by Parts

[anish]

I tried this using substitution and got a different answer. U need to integrate (u-1)*u^5 which is the same as integrating u^6 - u^5 and when u integrate this u get u^7/7 - u^6/6.

[ines]

Why can I not use inspection for 1/6(x+1)^6 since I keep getting 1/7(x+1)^7

[harrysmith]

How would you do this by substitution please?

I tried using u=x+1 and I get u'=1 so du=dx
This gives me the integral of xu^5 du
which I don't know how to solve

[tearman]

Great explanation!! However, the book I'm studying on tells me to factorise the final result and I have no clue how to do it. Could you please tell me? Thanks

[ninanakagawa]

why it works with u substitution & integration by parts? as i know substitution only works for ∫ g'(x). f(g(x))