# Integration

• December 10th 2013, 05:13 PM
leibnitz
Integration
Pls fans help me out with this problem........n3/square root n+1

• December 10th 2013, 05:17 PM
romsek
Re: Integration
what's the question?
• December 10th 2013, 05:54 PM
topsquark
Re: Integration
Quote:

Originally Posted by leibnitz
Pls fans help me out with this problem........n3/square root n+1

I think you attached the wrong file?

-Dan
• December 10th 2013, 07:25 PM
Prove It
Re: Integration
Assuming the OP meant to write \displaystyle \begin{align*} \int{ \frac{ n^3 }{ \sqrt{ n + 1 }}\,dn} \end{align*}, a substitution of the form \displaystyle \begin{align*} u = n + 1 \implies du = dn \end{align*} is appropriate, giving

\displaystyle \begin{align*} \int{ \frac{n^3}{\sqrt{n+1}}\,dn} &= \int{ \frac{\left( u - 1 \right) ^3}{\sqrt{u}}\,du} \end{align*}

Now expand the numerator, divide each term by \displaystyle \begin{align*} u^{\frac{1}{2}} \end{align*}, and integrate.