1. ## help with integration!

Really need help! How do I integrate 4/(sqrt(x)sqrt(1-x)) and e^(-x)cosx? I tried using algebraic manipulation for the first one and integration by parts for the second, got a mess of workings, really will appreciate your help!

2. ## Re: help with integration!

Hey Tutu.

Try using the fact that SQRT(x)*SQRT(1-x) = SQRT(x - x^2) and then complete the square.

Hint: Completing the square for ax^2 + bx is adding the term (0.5*b/SQRT(a))^2 and also -(0.5*b/SQRT(a))^2 to get (SQRT(a)*x + 0.5*b/SQRT(a))^2 - (0.5*b/SQRT(a))^2.

3. ## Re: help with integration!

Thanks! Couof you help ke with also the second one, thanks so much!

4. ## Re: help with integration!

For the second on try integration by parts by integrating the the trigonometric term twice (in other words do by parts twice) and then collect terms.

5. ## Re: help with integration!

Solution for the second integral is given in the attached sheet.
Be careful in selecting the first and second function while integrating by parts.

6. ## Re: help with integration!

Hi thanks a lot for both your help! I am confused though, according to the LIATE rule,
u should be cos(x) since trigo functions come before exponential, isn't it?

7. ## Re: help with integration!

In this case it won't make any difference, as exponential functions only change by a constant multiple when differentiated or integrated, and sine and cosine functions repeat each other by constant multiples after being differentiated or integrated twice.