` cos ^(3) x e ^(log sin x )`

cos^(3) x e^(log sinx)

cos^(3) x e^(log sinx)

cos^3x e^(log sin x)

Integrate the function cos ^3x e^(log sin x)

If u=e ^(log cos 4x ),v =e ^(log sin 4x ),then (dv)/(du)=

int (cos x)/( sin x log sin x)dx=

int (sin x + cos x)/( e^(-x) + sin x) dx is equal to a) log | 1-e^(x) sin x| +C b) log | 1 + e^(-x) sin x| + C c) log | 1+e^(x) sin x| + C d) log | 1 -e^(-x) sinx | +C

Prove that : int_(0)^(pi//2) (sin x -cos x) log (sin^(3) x + cos^(3)x) dx=0

Prove that : int_(0)^(pi//2) (sin x -cos x) log (sin^(3) x + cos^(3)x) dx=0

Differentiate the following w.r.t x: (i) e^(-x) (ii) sin (log x), x gt 0 (iii) cos^(-1) (e^(x)) (iv) e^(cos x)