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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.
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