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What is the integral of #int sin^3 (x)cos^3 (x) dx#?

Answer 1

#int sin^3 x cos^3 x d x=1/4sin^4 x-1/5sin^5 x+C#

#int sin^3 x cos^3 x d x= ? " "sin x=u" "cos x d x=d u# #int sin^3 x* cos^2 x* cos x* d x" "cos^2 x=1-sin^2 x# #int u^3(1-sin^2)d u" "int u^3(1-u^2) d u" "int(u^3-u^5)d u# #int sin^3 x cos^3 x d x=1/4u^4-1/5u^5+C# #int sin^3 x cos^3 x d x=1/4sin^4 x-1/5sin^5 x+C#

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Answer 2

Luke Alvarez

The integral of sin^3(x) * cos^3(x) dx is:

∫ sin^3(x) * cos^3(x) dx = -1/3 * cos^6(x) + 1/3 * cos^4(x) + C

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.