Find the integral of: sin^4(x)*cos(x)dx
This is a standard integral of the type f'(x)*f(x)n. To find the solution, we trial d/dx(f(x)n+1). d/dx(sin5(x)) = 5sin4(x)cos(x). this looks similar to the integral we were asked to solve, apart from a factor of 5. so we multiply by 5 inside the integral, and divide by 5 outside the integral. now that the inside of the integral looks like 5sin4(x)cos(x), we know this integrates into sin5(x). so the solution is (1/5)*sin5(x)
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