What's the integral of sin^3(x)cos(x)?

The integral of sin^3(x)cos(x) is (-1/4)cos^4(x) + C.

To solve this integral, we can use the substitution u = sin(x), du = cos(x)dx. Then the integral becomes:

∫sin^3(x)cos(x)dx = ∫u^3du

Integrating u^3, we get:

(1/4)u^4 + C = (1/4)sin^4(x) + C

Substituting back in for u, we get:

(-1/4)cos^4(x) + C

Therefore, the integral of sin^3(x)cos(x) is (-1/4)cos^4(x) + C.