Integral of the power products, solve the following integral: (sin^3sqrt(x))/sqrt(x)dx ?
1 Answer
Apr 5, 2018
Explanation:
We want to solve
I=intsin^3(sqrt(x))/sqrt(x)dx
Make a substitution
I=intsin^3(u)/sqrt(x)*2sqrt(x)du=2intsin^3(u)du
By the Pythagorean trig identity
I=2intsin(u)(1-cos^2(u))du
color(white)(I)=2intsin(u)du-2intsin(u)cos^2(u)du
For the second integral substitute
I=2intsin(u)du+2ints^2ds
color(white)(I)=-2cos(u)+2/3s^3+C
Substitute back
I=-2cos(sqrt(x))+2/3cos^3(sqrt(x))+C