Integrate? S10/√(2+√x)dx
1 Answer
Mar 2, 2018
Explanation:
I assume you mean, and the S is meant as an integral sign :)
I=int10/(sqrt(2+sqrt(x)))dx
Make a substitution
I=int10/(sqrt(u))2sqrt(x)dx
But
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
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