integral of cos^3(x)sin(x)

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(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

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∫ cos³(x)sin(x)dx

Solution

−cos⁴(x)4 +C

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Solution steps

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∫ cos³(x)sin(x)dx

Apply u-substitution: ∫ −u³du

=∫ −u³du

Take the constant out: ∫a·f(x)dx=a·∫f(x)dx

=−∫ u³du

Apply the Power Rule: u⁴4

=−u⁴4

Substitute back u=cos(x)

=−cos⁴(x)4

Add a constant to the solution

=−cos⁴(x)4 +C

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integral of cos^3(x)sin(x)

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