# How do you integrate #(sin x)/(1+sin x)^2#?

This is one of the most difficult integrals I've seen in a long time. Given that I know the solution from Wolfram Alpha, I believe I have a good start on it. Can someone assist me in finishing it?

Wolfram Alpha generates the following: https://tutor.hix.ai

I'll continue to work on it, and I'd advise others to do the same.

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

It would be fantastic to see if someone else could solve the algebra more cleverly or has a better idea.

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

To integrate (\frac{\sin x}{(1+\sin x)^2}), you can use the substitution method. Let (u = 1 + \sin x), then (du = \cos x dx). After substitution, the integral becomes (\int \frac{1}{u^2} du), which is straightforward to integrate. The final result will be (-\frac{1}{1+\sin x} + 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.

- How do you find the integral of #int sin^3(x)dx#?
- How do you use limits to find the area between the curve #y=x^2+6x# and the x axis from [0,4]?
- How do you find the definite integral for: #(sqrt(b^2-a^2)) da# for the intervals #[0, b]#?
- How do you integrate #int x/(sqrt(2x-1))dx# from [1,5]?
- How do you find the definite integral for: #(x^43) (e^(-x^(44)) dx)# for the intervals #[0, 1]#?

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