The integral ∫ x√(x²+a²)dx, where a>0, can be effectively solved using u-substitution rather than trigonometric substitution. The substitution u=x²+a² leads to du=2xdx, simplifying the integration process. While trigonometric methods are available, they complicate the solution and require additional substitutions. Therefore, u-substitution is the recommended approach for this problem.
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Xetman said:Homework Statement
http://i50.tinypic.com/zxw6qr.png
a>0
a
∫ x√(x^2+a^2)dx (a>0)
0
2. The attempt at a solution
u=x^2+a^2
du=2xdx
I looked it up online and I saw you needed to use trig.
How do you use trig for this problem?
Note: I have not learned integration by parts, just u-sub.
As Dick said, you can just continue with your u-sub and you'll find the problem can be solved relatively easily. Now, you could solve it by using trig substitution but it does become more difficult, and you'd need to do 2 substitutions as well.Xetman said:Homework Statement
http://i50.tinypic.com/zxw6qr.png
a>0
a
∫ x√(x^2+a^2)dx (a>0)
0
2. The attempt at a solution
u=x^2+a^2
du=2xdx
I looked it up online and I saw you needed to use trig.
How do you use trig for this problem?
Note: I have not learned integration by parts, just u-sub.