How do you use substitution to integrate $x^2sqrt(x+1)$ ?

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Answer 1 · 2015-09-25T05:18:36

Refer to explanation

We set $u=sqrt(x+1)$ hence $du=1/(2*sqrt(x+1))dx$

$int x^2*sqrt(x+1)dx=2*int (u^2-1)^2*u^2du= 2*int (u^6-2u^4+u^2)du=2*[u^7/7-2*u^5/5+u^3/3]$

Now replacing u with $sqrt(x+1)$ we get finally that

$int x^2*sqrt(x+1)dx=2/105*sqrt((x+1)^3)*(15x^2-12x+8)+c$

How do you use substitution to integrate x^2sqrt(x+1)x^2sqrt(x+1)?