Integration question with power of n

1. Oct 24, 2012

http://www.xtremepapers.com/papers/...S Level/Mathematics (9709)/9709_w11_qp_33.pdf1. The problem statement, all variables and given/known data
no. 10i
cant do ii and iii without doing i first

2. Relevant equations
tan(x)
d/dx(tan(x))=sec^2x
1+tan^2x=sec^2x

3. The attempt at a solution
Okay, my terms at first would be u^n+2 +u^n. Then, du/dx = sec^2x, so i get du/1+u^2 = dx.

In the end i got (u^n+2 +u^n)/1+u^2. From then on im stuck. Or did i do something wrong at first?

2. Oct 24, 2012

Arkuski

You know that u=tan[x] so du=sec2[x]dx.

Let's rearrange the integral a little bit to show the following:

∫tann[x](tan2[x]+1)dx

Remember that dx=du/sec2[x]. However, we need to find sec2[x] in terms of u. We use the following identity of sec2[x]=tan2+1 to show now that dx=du/(u2+1)

∫un(u2+1)/(u2+1)=∫un

This now becomes a simple integration problem and you should be able to do the rest.

3. Oct 24, 2012