Solve this Solve this ∫ sin2x cos4x dx - Maths - Integrals

Question

Solve this

Solve this ∫   sin 2 x  cos 4
x  dx

Rahul Raj · Accepted Answer

dear student

I=∫sin2xcos4xdx=∫1-cos2x21+cos2x22dx=18∫(1-cos2x)(1+cos22x+2cos2x)dx=18∫(1+cos22x+2cos2x-cos2x-cos32x-2cos22x)dx=18∫(1-cos22x+cos2x-cos32x)dx=18∫(1-1+cos4x2+cos2x-cos22x
cos2x)dx=18(x/2-sin4x/8+sin2x/2-∫(1-sin22x)cos2xdx)+c=18(x/2-sin4x/8+sin2x/2-12(sin2x-sin32x3))+c

regards

Solve this. Solve this. ∫ sin 2 x cos 4 x dx

Solve this.

Solve this. $\int {sin}^{2} {x cos}^{4} x dx$