(adsbygoogle = window.adsbygoogle || []).push({}); 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

Now i tried all the methods i know of which include integration by parts and substitution,the integration by parts didn't work too well, so substitution I tried.

let [tex]u=tan^2x[/tex] and [tex]du = 2tanxsec^2x[/tex]

eventually giving me

[tex]\int tan^4xsec^3x dx[/tex] which i can't do

and if I used [tex]u^2=x+1[/tex] I eventually get

[tex]2\int u^3(u^2-1)^\frac{3}{2} du[/tex] which i also can't do

is there any useful substitution i can do?

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# How to integrate a function with a square root in it

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