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int(0)^(2 pi)e^(x)cos((pi)/(4)+(x)/(2))d...

int_(0)^(2 pi)e^(x)cos((pi)/(4)+(x)/(2))dx

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int_(0)^(2pi)e^(x) (x/2+pi/4) dx =

int_(0)^(2pi)e^(x//2)sin((x)/(2)+(pi)/(4))dx=

int_(0)^(2 pi)|cos x|dx

int_(0)^(2pi)e^(x/2).sin(x/2+(pi)/4)dx=

int_(0)^( pi)(x)/(4-cos^(2)x)dx

u,=int_(0)^((pi)/(2))cos((2 pi)/(3)sin^(2)x)dx and v,=int_(0)^((pi)/(2))cos((pi)/(3)sin x)dx

If A=int_(0)^( pi)(cos x)/((x+2)^(2))dx, then int_(0)^( pi/2)(sin2x)/(x+1)dx is equal to

int_(0)^(2pi) e^(x//2) sin (x/2 + pi/4) dx=

int_(0)^( pi)|cos x|dx=2