E_n = int((2*x/Pi)^(2*n)*cos(x), x = -(1/2)*pi .. (1/2)*pi)

I'm supposed to use integration by parts to make a reduction formula for E_n but it seems to just make it more complicated. Can somebody help me figure this out?

Question

E_n = int((2*x/Pi)^(2*n)*cos(x), x = -(1/2)*pi .. (1/2)*pi)

I'm supposed to use integration by parts to make a reduction formula for E_n but it seems to just make it more complicated.  Can somebody help me figure this out?

turingtest · Answer

$$E_n=\int_{2x/\pi}^{2n}\cos x dx$$$$-\frac\pi2\le x\le\frac\pi2$$did I type this right?