# How do you integrate #(cosx)^2dx#?

Considering that:

Integrating by parts:

So:

and finally:

An alternative method is to use the identity:

so that:

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To integrate (cosx)^2 dx, you can use the trigonometric identity:

cos^2(x) = (1 + cos(2x))/2.

Then, the integral becomes:

∫ (cosx)^2 dx = ∫ (1 + cos(2x))/2 dx.

This simplifies to:

(1/2) ∫ (1 + cos(2x)) dx.

Integrate term by term:

(1/2) ∫ dx + (1/2) ∫ cos(2x) dx.

Integrating each term:

(1/2) * x + (1/4) * sin(2x) + C.

So, the integral of (cosx)^2 dx is:

(1/2) * x + (1/4) * sin(2x) + C, where C is the constant of integration.

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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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