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!

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- December 28th 2012, 11:03 PMTutuhelp 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!

- December 28th 2012, 11:22 PMchiroRe: 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. - December 28th 2012, 11:59 PMTutuRe: help with integration!
Thanks! Couof you help ke with also the second one, thanks so much!

- December 29th 2012, 12:03 AMchiroRe: 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.

- December 29th 2012, 02:21 AMibduttRe: 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.

Attachment 26400 - December 29th 2012, 06:42 AMTutuRe: 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? - December 29th 2012, 06:38 PMProve ItRe: 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.