Pls fans help me out with this problem........n^{3}/square root n+1

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- Dec 10th 2013, 05:13 PMleibnitzIntegration
Pls fans help me out with this problem........n

^{3}/square root n+1

- Dec 10th 2013, 05:17 PMromsekRe: Integration
what's the question?

- Dec 10th 2013, 05:54 PMtopsquarkRe: Integration
- Dec 10th 2013, 07:25 PMProve ItRe: Integration
Assuming the OP meant to write $\displaystyle \displaystyle \begin{align*} \int{ \frac{ n^3 }{ \sqrt{ n + 1 }}\,dn} \end{align*}$, a substitution of the form $\displaystyle \displaystyle \begin{align*} u = n + 1 \implies du = dn \end{align*}$ is appropriate, giving

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

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