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