Integration Help: Solve ∫sqrt(a^2-x^2)/x*sqrt(x^2-b^2)

[WiFO215]

Homework Statement

\int \sqrt{a^{2}-x^{2}}/x*\sqrt{x^{2}-b^{2}}

The Attempt at a Solution

I tried all sorts of substitutions and none work. Please help me.

 

[HallsofIvy]

Would it help to know that
\frac{a^2- x^2}{x^2- b^2}= \frac{b^2- a^2}{x^2- b^2}- 1

 

[WiFO215]

Edit notice: I multiplied the integrand by 1/x. Its not to the xth root of. I didn't type that in first type.

 

[WiFO215]

I don't have a clue how that helps HallsofIvy.

 

[WiFO215]

Mathematica says this rubbish can't be solved.

 

[HallsofIvy]

Have you editted the first post? I didn't notice that "x" outside the square root before.
Let u= x²- b² so that du= 2xdx
\sqrt{\frac{b^2-a^2}{x^2- b^2}-1}= \sqrt{\frac{A}{u}- 1}

 

[WiFO215]

Yes. I edited the first post. Forget it though. I think what I did is wrong anyway.