# How do you integrate #int cos^3x dx#?

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To integrate ( \int \cos^3(x) , dx ), you can use the trigonometric identity ( \cos^2(x) = 1 - \sin^2(x) ). Then, perform a substitution by letting ( u = \sin(x) ). This will change ( du = \cos(x) , dx ). With these substitutions, the integral becomes ( \int (1 - u^2) , du ). Integrating term by term, you get ( u - \frac{u^3}{3} + C ), where ( C ) is the constant of integration. Finally, revert back to the variable ( x ) using ( u = \sin(x) ). Thus, the solution is ( \sin(x) - \frac{\sin^3(x)}{3} + C ).

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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.

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.

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.

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