What's the integral of sin(x)cos^4(x)?

The integral of sin(x)cos^4(x) is (-1/5)cos^5(x) + C.

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

∫sin(x)cos^4(x)dx = -∫u^4du

Integrating this expression gives:

-∫u^4du = (-1/5)u^5 + C

Substituting back u = cos(x), we get:

(-1/5)cos^5(x) + C

Therefore, the integral of sin(x)cos^4(x) is (-1/5)cos^5(x) + C.