Integrate? S10/√(2+√x)dx

1 Answer
Mar 2, 2018

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