# How do you integrate #int e^(2x)/(1+e^(2x))dx#?

The answer is

Let's do it by substitution

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

To integrate ( \int \frac{e^{2x}}{1+e^{2x}} , dx ), we can use a substitution method. Let ( u = 1 + e^{2x} ). Then, ( du = 2e^{2x} , dx ). Solving for ( dx ), we get ( dx = \frac{du}{2e^{2x}} ). Substituting these into the integral gives:

[ \int \frac{e^{2x}}{1+e^{2x}} , dx = \int \frac{1}{u} \cdot \frac{du}{2e^{2x}} = \frac{1}{2} \int \frac{1}{u} , du ]

This integral is straightforward to solve. After integrating, we resubstitute ( u ) back in terms of ( x ) to get the final result.

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 use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function #h(x)=int_4^(1/x) arctan(3t) dt#?
- How do you integrate #(x+2)/(2x^3-8x)# using partial fractions?
- How do you use summation notation to expression the sum #32+24+18+...+10.125#?
- How do you evaluate the integral #int 1/(x-1)^(2/3)dx# from 0 to 2?
- What is the net area between #f(x)=ln(x+1)# in #x in[1,2] # and the x-axis?

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