Integrate x/sqrt(a^2+b^2-2abx)

[albega]

Homework Statement

I need to integrate x/sqrt(a^2+b^2-2abx) with respect to x.

The Attempt at a Solution

This follows from a substitution of the form x=cost in a textbook I'm reading - they jump to the solution straight from the above and I have no idea how to go about it - any hints will be very gratefully appreciated, thanks :)

 

[pasmith]

Homework Statement

I need to integrate x/sqrt(a^2+b^2-2abx) with respect to x.

The Attempt at a Solution

This follows from a substitution of the form x=cost in a textbook I'm reading - they jump to the solution straight from the above and I have no idea how to go about it - any hints will be very gratefully appreciated, thanks :)

Hint: $$\int \frac{Au + B}{\sqrt u}\,du = \int Au^{1/2} + Bu^{-1/2}\,du.$$

 

[albega]

Hint: $$\int \frac{Au + B}{\sqrt u}\,du = \int Au^{1/2} + Bu^{-1/2}\,du.$$

Got it, thanks! Was that something you could spot or did you just know it from experience - I don't think I would ever have thought of something like that...

 

[SteamKing]

You also should make an attempt to post HW in the correct HW forum. There is a perfectly good Calculus-HW forum listed right below this one, which is where this post belongs.

 

[berkeman]

You also should make an attempt to post HW in the correct HW forum. There is a perfectly good Calculus-HW forum listed right below this one, which is where this post belongs.

Thread moved to Calculus HH.