# How do you find the integral of #cos(x)/(5+sin^2(x))dx#?

You should recognize the right side as the inverse tangent form:

Reverse the substitution for u:

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To find the integral of ( \frac{\cos(x)}{5+\sin^2(x)} ) with respect to ( x ), you can use the substitution method. Let ( u = \sin(x) ). Then ( du = \cos(x) , dx ). Substituting these into the integral, you get ( \int \frac{1}{5+u^2} , du ). This is a standard integral, which evaluates to ( \frac{1}{\sqrt{5}} \arctan\left(\frac{u}{\sqrt{5}}\right) + C ), where ( C ) is the constant of integration. Finally, substitute ( u = \sin(x) ) back in to get the final answer in terms of ( x ).

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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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