# How do I integrate the function #f(x)=cos(x)/(sin^2(x))+sin(x)#?

By signing up, you agree to our Terms of Service and Privacy Policy

Try this:

By signing up, you agree to our Terms of Service and Privacy Policy

To integrate the function ( f(x) = \frac{\cos(x)}{\sin^2(x)} + \sin(x) ), you can use the method of substitution. Let ( u = \sin(x) ), then ( du = \cos(x)dx ). After substitution, the integral becomes ( \int \frac{1}{u^2} du + \int u du ).

Integrating each term separately, you get ( -\frac{1}{u} + \frac{u^2}{2} + C ), where ( C ) is the constant of integration.

Now, substituting back ( u = \sin(x) ), you get ( -\frac{1}{\sin(x)} + \frac{\sin^2(x)}{2} + C ).

So, the indefinite integral of ( f(x) ) is ( -\csc(x) + \frac{\sin^2(x)}{2} + C ), where ( C ) is the constant of integration.

By signing up, you agree to our Terms of Service and Privacy Policy

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.

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7