# How do you integrate #int sinx/(2+3cosx)^2# using substitution?

The answer is

Therefore,

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To integrate ( \int \frac{{\sin x}}{{(2 + 3\cos x)^2}} ) using substitution:

- Let ( u = 2 + 3\cos x ).
- Find ( du = -3\sin x , dx ).
- Rewrite the integral in terms of ( u ) and ( du ).
- The integral becomes ( -\frac{1}{3} \int \frac{1}{u^2} , du ).
- Integrate ( \frac{1}{u^2} ) with respect to ( u ).
- The result is ( -\frac{1}{3} \left(-\frac{1}{u}\right) + C ).
- Substitute back ( u = 2 + 3\cos x ) into the result.
- The final answer is ( \frac{1}{3(2 + 3\cos x)} + 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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