SOLUTION: find integrals: sin^3 (x) cos^2(x) . dx the key is ; (1/5) cos^5 (x) -(1/3) cos^3 (x) + c thank

Question 707038: find integrals: sin^3 (x) cos^2(x) . dx
the key is ; (1/5) cos^5 (x) -(1/3) cos^3 (x) + c
thank
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

First factor the sin's:

Then replace with :

Then multiply:

Separate into two integrals:

Since the derivative of cos is -sin we almost have cos to some power times the derivative of cos in each integral. We just need the factors of -1:

"Pulling" the unwanted -1's outside the integrals:

which simplifies to:

Now we have cos to some power times the derivative of cos. These are now simple integrals:

which is equivalent to the answer you provided.
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