# Need help finding an antiderivative

• leesa
In summary, to find the antiderivative of 36/ (2x + 1) ^3, use u-substitution with u=2x+1. This will allow you to integrate the expression and find the answer. Remember, there are no stupid questions when it comes to learning!
leesa
need help finding an antiderivative!

## Homework Statement

1
∫ 36/ (2x + 1) ^3 dx
0
I just can't figure out how to take the antiderivative of this! What do I do with the (2x +1) ^3??

leesa said:

## Homework Statement

1
∫ 36/ (2x + 1) ^3 dx
0
I just can't figure out how to take the antiderivative of this! What do I do with the (2x +1) ^3??

## The Attempt at a Solution

set u=2x+1 and do u-substitution

ok! I get it. I was looking in the wrong part of the book and I thought the directions said to use part 2 of the fundamental theorem! So I was freaking out because I was sure the theorem couldn't be used for this. thanks! sorry I asked a stupid question.

haha no problem. there are no stupid questions!

## 1. What is an antiderivative?

An antiderivative is the inverse operation of a derivative. It is a function that, when differentiated, gives the original function.

## 2. Why is finding an antiderivative important?

Finding an antiderivative allows us to solve indefinite integrals, which are essential in many areas of mathematics and science, including physics, engineering, and economics.

## 3. How do I know when I need to find an antiderivative?

If you are given a function and asked to find the area under its curve, you will need to find the antiderivative to solve the integral.

## 4. What are some common techniques for finding an antiderivative?

Some common techniques include the power rule, substitution, and integration by parts. It is also helpful to know the basic antiderivatives of common functions.

## 5. Is there a general method for finding an antiderivative?

Yes, the Fundamental Theorem of Calculus provides a general method for finding antiderivatives. It states that if a function is continuous on an interval, then its antiderivative can be found by evaluating the function at the upper and lower limits of the interval and subtracting the results.

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