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Out of a number of trig integrals I have been working on, there are a few I'm having trouble with. I have the answers for them but am unsure of how to proceed to reach that point.
Integral of (tan(x/2)sec(x/2))^3 dx
Answer: (2/5)sec^5(x/2) - (2/3)sec^3(x/2) + c
Integral of csc^5x dx
Answer: (-1/4)cotxcsc^3x - (3/8)cotxcscx + (3/8) ln(cscx-cotx) + c
Integral of cos(3x)cos(5x) dx
Answer: (1/4)sin(2x) + (1/16)sin(8x) + c
The final one is rather tricky.
I am not sure whether it reads:
Integral from 0 to pi/2 of sin(3x/2)sin(x/2) dx
Integral from 0 to pi/2 of sin^(3/2)(x)sin^(1/2)(x) dx
Either way the answer given is: (1/2)
Thanks in advance for any help given