Question

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

Answer 1

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

Explanation:

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`