e^(x)+2sin x-3cos x

The value of int e^((x sin x+ cos x)).((x^(4)cos^(3)x-x sin x + cos x)/(x^(2)cos^(2) x)) dx , is equal to

(sin^(3)x+cos^(3)x)/(sin x+cos x)+(sin^(3)x-cos^(3)x)/(sin x-cos x)=2

sin^(2)x+2sin x cos x-3cos^(2)x=0 if

If a sin^(3)x+b cos^(3)x= sin x cos x and a sin x= b cos x then a^(2)+b^(2)=

int e^(2x)(-sin x+2cos x)dx

The value of int e^(2x) (2sin 3x + 3 cos 3x) dx is

int (sin x * e ^ (cos x) - (sin x + cos x) e ^ (sin x + cos x)) / (e ^ (2sin x) -2e ^ (sin x) +1) dx

Delta (x) = det [[sin2x, e ^ (x) sin x + x cos x, sin x + x ^ (2) cos xcos x + sin x, e ^ (x) + x, 1 + x ^ ( 2) e ^ (x) cos x, e ^ (2) x, e ^ (x)]]

Delta (x) = det [[sin2x, e ^ (x) sin x + x cos x, sin x + x ^ (2) cos xcos x + sin x, e ^ (x) + x, 1 + x ^ ( 2) e ^ (x) cos x, e ^ (2) x, e ^ (x)]]