[,Delta(x),,],[,,Delta(x)],[,|[sin2x,e^(x)sin x+x cos x,sin x+x^(2)cos],[cos x+sin x,e^(x)+x,1+x^(2)],[e^(x)cos x,e^(2x),e^(x)]]

int e^(2x) sin x cos x 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)]]

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

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

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

int e^(x)sin x cos x cos2x cos4x.dx

e^(x)((2+ sin 2x)/(1 + cos 2 x ))

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