Integration problem~ (1 Viewer)

[YannY]

Hey - how do we integrate In=f(x^n . tan-1 x)

These questions takes forever and are always so messy.

Thanks.

 

[rooeys2]

omg ur doin integration already
u scare me yang

 

[Trebla]

I can do it easily with Taylor series but you don't cover that at school...

 

[Yip]

Taylor series expansion is not the best way to approach this problem as it gives an infinite series even for small values of n. Its just an integration by parts problem.

I=[1/(n+1)]x^(n+1)arctanx-[1/(n+1)]∫x^(n+1)/(1+x^2)dx

A reduction can be formed for ∫x^(n+1)/(1+x^2)dx:
J[n+1]=∫x^(n+1)/(1+x^2)dx =∫x^2*x^(n-1)/(1+x^2)dx
=∫[x^(n-1)-[x^(n-1)/(1+x^2)]]dx=(1/n)x^n-J[n-1]

the end result is rather messy for large n.

 

[YannY]

We started integration this week.

It's okay. Not great. Not to hard for now either.

Haven't done that question you asked about though.

Yes... very interesting - what school do you go to?

 

[danielle69]

H.W.M.H.S.

omg me too lol

 

[YannY]

H.W.M.H.S.

Whats this? Honky western masters high school?