(adsbygoogle = window.adsbygoogle || []).push({}); Integral with sq. root in it....again

1. The problem statement, all variables and given/known data

Find..

[tex]\int x^\frac{3}{2}\sqrt{1+x} dx[/tex]

2. Relevant equations

3. The attempt at a solution

Well I used the fact that:

[tex]\sqrt{1+x}=\sum_{n=0} ^\infty \frac{(-1)^n(2n!)x^n}{(1-2n)(n!)^24^n}[/tex]

and well I just multiplied by [itex]x^\frac{3}{2}[/itex]

so I integrated:

[tex]\int \sum_{n=0} ^\infty \frac{(-1)^n(2n!)x^(n+\frac{3}{2}}{(1-2n)(n!)^24^n}[/tex]

and got [tex]\sum_{n=0} ^\infty \frac{(-1)^n(2n!)x^(n+\frac{5}{2}}{(1-2n)(n!)^24^n\frac{5}{2}}[/tex]

[itex]\frac{2x^\frac{5}{2}}{5}\sqrt{1+x}[/itex] which is wrong because if i differentiate it I get an extra term in it

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# Homework Help: Integral with sq. root in it again

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