integration by substitution

**daaavo** · March 6th 2008, 05:16 PM

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

**TheEmptySet** · March 6th 2008, 05:22 PM

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...

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

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