`e^(-2x)sin 4 x`

e^(-4x) sin 2 x

e^(-3x) sin 2x

e^(2x) sin 3x

Integrate : int e^(-2x) sin 3x sin 4x dx

e^(3x).sin4x

int e^(2x) sin x dx

int e ^ (2x) ((sin4x-2) / (1-cos4x)) dx

(i) int e^(2x) ((1+sin2x)/(1+cos2x)) dx (ii) int e^(2x) ((sin4x-2)/(1-cos4x))

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)]]