Question

Integrate? S10/√(2+√x)dx

Answer 1

`I=40/3(2+sqrt(x))^(3/2)-80sqrt(2+sqrt(x))+C`

Explanation:

I assume you mean, and the S is meant as an integral sign :)

`I=int10/(sqrt(2+sqrt(x)))dx`

Make a substitution `u=2+sqrt(x)=>(du)/dx=1/(2sqrt(x))`

`I=int10/(sqrt(u))2sqrt(x)dx`

But `u=2+sqrt(x)=>sqrt(x)=u-2`

`I=int10/(sqrt(u))2(u-2)dx=20intsqrt(u)-2/sqrt(u)du`

Integrate

`I=20(2/3u^(3/2)-4sqrt(u))+C`

Substitute back `u=2+sqrt(x)`

`I=20(2/3(2+sqrt(x))^(3/2)-4sqrt(2+sqrt(x)))+C`

`I=40/3(2+sqrt(x))^(3/2)-80sqrt(2+sqrt(x))+C`