How do you use substitution to integrate $f(x)= x/sqrt(20+x^2)$ ?

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Answer 1 · 2018-03-12T09:30:02

$int x/sqrt(20+x^2)dx = sqrt(20+x^2)+C$

Substitute $u = 20+x^2$ , $du = 2xdx$

$int x/sqrt(20+x^2)dx = 1/2 int (2xdx)/sqrt(20+x^2) = int (du)/(2sqrtu) = sqrt(u)+C$

and undoing the substitution:

$int x/sqrt(20+x^2)dx = sqrt(20+x^2)+C$

How do you use substitution to integrate f(x)= x/sqrt(20+x^2) f(x)= x/sqrt(20+x^2)?