# Math Help - integration by substitution

1. ## integration by substitution

would you possibly be able to show me a step by step solution for the following??

Integrate: 2x((x^2)+1)^23 dx with respect to x

thanks

Dave

2. Originally Posted by daaavo
would you possibly be able to show me a step by step solution for the following??

Integrate: 2x((x^2)+1)^23 dx with respect to x

thanks

Dave
Try the u substition

$u=x^2+1$ then $du=2xdx$

so making the substition

$\int 2x(x^2+1)^{23}dx=\int u^{23}du=\frac{1}{24}u^{24}+C$

subbing u back in we get...

$\frac{1}{24}(x^2+1)^{24}+C$