# How do you find the antiderivative of #e^(2x + 1)# dx?

Remembering the rule:

than

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

To find the antiderivative of ( e^{2x + 1} , dx ), you can use the technique of integration by substitution. Let ( u = 2x + 1 ). Then, ( du/dx = 2 ), and thus ( dx = du/2 ). Substituting these expressions into the original integral, we have:

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

The antiderivative of ( e^u ) with respect to ( u ) is simply ( e^u ), so:

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

Finally, resubstituting back ( u = 2x + 1 ), the antiderivative becomes:

[ \frac{1}{2} e^{2x + 1} + 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.

- What is #f(x) = int x^2e^(x-1)-x^3e^-x dx# if #f(2) = 7 #?
- How do you use substitution to integrate # (2x+3)/(x+7)^3 #?
- How do you integrate #int -x^3/sqrt(144+x^2)dx# using trigonometric substitution?
- How do you integrate #int (13x) / (6x^2 + 5x - 6)# using partial fractions?
- How do you integrate by substitution #int(x^2-9)^3(2x)dx#?

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