int_(-pi/4)^(n/4)log(sin x+cos x)dx

Evaluate: int_(-pi/4)^( pi/4)log(sin x+cos x)dx

Prove that int_(-pi/4)^( pi/4)log(sin x+cos x)backslash dx=-(pi)/(4)backslash log2

If I_(1) = int_(0)^(pi//2)ln (sin x)dx , I_(2)=int_(-pi//4)^(pi//4)ln (sin x + cos x)dx , then :

int_(0)^(pi//4)log ((sin x +cos x )/(cosx))dx is equal to

[int_(-pi/4)^( pi/4)log(cos x+sin x)dx=(1)/(2)],[[" 1) "pi log2," 2) "-pi log2," 3) "-(pi)/(4)log2," 4) "-(pi)/(2)log2]]

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

Evaluate the following integrals: underset(-pi//4)overset(pi//4)int log(sin x + cos x) dx

int _(0)^(pi//4) log ((sin x+ cos x)/(cosx))dx is equal to

int_0^(pi/4) (cos x- sin x) dx + int_(pi/4)^((5pi)/4) (sinx-cosx) dx + int_(2pi)^(pi/4) (cosx- sinx) dx =

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