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" 39."int(0)^( pi)[cos^(2)((3 pi)/(8)-(x...

" 39."int_(0)^( pi)[cos^(2)((3 pi)/(8)-(x)/(4))-cos^(2)((11 pi)/(8)+(x)/(4))]dx

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int _(0) ^(pi)[ cos ^(2) ((3pi)/(8) - (x )/(4)) - cos ^(2) ((11pi)/(8)+ (x )/(4))] dx

int_(0)^(pi) cos^(8) x dx=

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

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

Find int_(0)^(pi//2) cos^(8)x dx

int_(0)^(pi//8) cos^(6) 4 x dx=

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

int_(0)^(pi//2)(dx)/((4+9cos^(2)x))

cos^4(pi/8)+cos^4((3pi)/8)+cos^4((5pi)/8)+cos^4((7pi)/8)=