# Finding the Antiderivative of a Reciprocal: Step-by-Step Guide

• cemar.
In summary, the conversation suggests that the person is struggling with finding the antiderivative of 1/(x+3)^2, despite it being an easy problem. They have attempted using partial fractions but are not confident in their approach. They are advised to review the chapter on "Techniques of Integration" and focus on u-substitution as the first method to try. The person acknowledges their need for a review and is planning to do so after their midterm. They also express that using sledgehammers is more enjoyable than using nutcrackers, but it is important to stay grounded and keep things simple. Overall, the conversation highlights the person's difficulty in finding the antiderivative and their determination to improve their understanding of calculus.
cemar.
1. Find the antiderivative of 1/(x+3)^2

Okayy i knwo this is an easy problem but i COMPLETELY forget how to do it.
Ive tried using partial fractions but it doesn't seem to be working.
I just need to know how to start the problem then i should be alright from there.
Thank you!

$$\int\frac{dx}{(x+3)^2}$$

$$u=x+3$$
$$du=dx$$

You need a major review! Makes no sense ... you can evaluate Integrals using Partial Fractions but yet you've forgotten basic u-sub? Weird.

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oh gosh.
IIIII'm just going to go hang myself right now.
Ill just use the excuse that I am smack dab in the middle of midterms thus in the state of mind that every thing is harder than it should be.
Thanks ... i definitely won't let myself make the same mistake again.

Tell him what you really think, roco!

cemar, he's right. By attempting to use partial fractions you're trying to use a sledgehammer when a nutcracker will do. You should hit the calc book and review the chapter entitled "Techniques of Integration" or something like that. Most calc books lay the material out in the order in which you should be thinking of them, kind of like a mental checklist. u-sub is invariably first, and that is the first thing you should try when confronted with a nonelementary antiderivative.

**her.
And thanks I am definitely planning on getting the hardcore review on after that slightly embarassing display of where I am at in calculus right now.
And for the record sledgehammers are a lot funner to use than nutcrackers.
=)

Lol, don't worry about it. You're stressed but remember, stay grounded and simple!

Wish you the best on your midterm :)

## 1. What is the definition of antiderivative of reciprocal?

The antiderivative of reciprocal is a function that, when differentiated, gives the reciprocal of the original function.

## 2. How is the antiderivative of reciprocal found?

The antiderivative of reciprocal can be found by using the power rule for integration, which states that the antiderivative of x^n is (1/(n+1))x^(n+1) + C.

## 3. What is the difference between the antiderivative of reciprocal and the integral of reciprocal?

The antiderivative of reciprocal is a specific function that, when differentiated, gives the original function. The integral of reciprocal, on the other hand, is a general term for any function that represents the area under a reciprocal curve.

## 4. Can the antiderivative of reciprocal be used to solve definite integrals?

Yes, the antiderivative of reciprocal can be used to solve definite integrals by plugging in the limits of integration and subtracting the result at the lower limit from the result at the upper limit.

## 5. Are there any special cases when finding the antiderivative of reciprocal?

Yes, there are some special cases when finding the antiderivative of reciprocal. For example, when the denominator of the reciprocal function is a constant, the antiderivative is (1/k)ln|x| + C. When the denominator is the square of a constant, the antiderivative is (-1/k)cos(kx) + C.

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