# Integrating (x² + 1)² using substitution

• Jul 29th 2012, 09:27 AM
SweatingBear
Integrating (x² + 1)² using substitution
Hey forum how would I go about in order to compute this indefinite integral,

$\displaystyle \int \, (x^2 +1)^2 \, \text{d}x \ ?$

I can't seem to eliminate all $\displaystyle x$-variables using $\displaystyle u = x^2 + 1$. I know I can simply compute it by expanding the integrand but I want to do it using substitution in particular.
• Jul 29th 2012, 09:42 AM
jeduhi
Re: Integrating (x² + 1)² using substitution
• Jul 29th 2012, 09:43 AM
Prove It
Re: Integrating (x² + 1)² using substitution
Quote:

Originally Posted by SweatingBear
Hey forum how would I go about in order to compute this indefinite integral,

$\displaystyle \int \, (x^2 +1)^2 \, \text{d}x \ ?$

I can't seem to eliminate all $\displaystyle x$-variables using $\displaystyle u = x^2 + 1$. I know I can simply compute it by expanding the integrand but I want to do it using substitution in particular.

You can't do this using substitution. Expand the integrand instead.
• Jul 29th 2012, 10:14 AM
Re: Integrating (x² + 1)² using substitution
Quote:

Originally Posted by Prove It
You can't do this using substitution.

How come?
• Jul 29th 2012, 10:27 AM
Prove It
Re: Integrating (x² + 1)² using substitution
Quote: