Integrate? S10/√(2+√x)dx

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Answer 1 · 2018-03-02T18:59:23

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

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#