`int_(0)^(pi//2) cosx\ e^(sinx)\ dx` is equal to

int _(0)^(pi//2) (cosx)/(1+sinx)dx is equal to

int_(0)^(pi//2) e^x(sinx+cosx) dx

The value of int_(0)^(2pi)|cosx-sinx|dx is equal to

int_(0)^(pi//2)(cosx)/(1+sinx)dx=

int_(0)^(pi//2)(cosx-sinx)e^(x)dx=

int_(0)^(pi//2) abs(sinx-cosx) dx=

int_(0)^(pi//4)(cosx-sinx)dx+int_(pi//4)^(5pi//4)(sinx-cosx)dx+int_(2pi)^(pi//4)(cosx-sinx)dx is equal to