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Homework Statement
find [tex] \int x^{\frac{3}{2}}\sqrt{1+x} dx [/tex]
Homework Equations
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?