# Thread: Finding The Most General Antiderivative

1. ## Finding The Most General Antiderivative

I am having a severe amount of trouble with the following question. I am unsure where to start or how to even tackle it. Thanks for any help

Find the most general antiderivative for the following function:

g(x) = (3-x²+(the square root of x) all over x to the power of 4.

I hope you could understand that, feel free to ask questions otherwise. Thanks again.

2. Originally Posted by GreenDay14
I am having a severe amount of trouble with the following question. I am unsure where to start or how to even tackle it. Thanks for any help

Find the most general antiderivative for the following function:

g(x) = (3-x²+(the square root of x) all over x to the power of 4.

I hope you could understand that, feel free to ask questions otherwise. Thanks again.
$\int \frac{3 - x^2 + \sqrt{x}}{x^4} \, dx = \int \frac{3}{x^4} - \frac{x^2}{x^4} + \frac{x^{1/2}}{x^4}\, dx$.

Simplify each term using the usual index laws and integrate in the usual way.

3. Sorry for the double post I thought I may have posted in the wrong section at first. As for your response to my question that does not really help me much I could have gotten that far but I am unsure how to get much farther.

4. Originally Posted by GreenDay14
Sorry for the double post I thought I may have posted in the wrong section at first. As for your response to my question that does not really help me much I could have gotten that far but I am unsure how to get much farther.
$\frac{3}{x^4} = 3 x^{-4}$.

$\frac{x^2}{x^4} = x^2$.

$\frac{x^{1/2}}{x^4} = x^{-7/2}$.

It's expected that you can simplify expressions such as these using index laws. It's expected that you can integrate each of these things.

5. If it is not to much to ask, could you possibly link me to a site explaining the index laws or something? Because i have no idea what you are referring to. Thanks for the help tho.

6. Originally Posted by GreenDay14
If it is not to much to ask, could you possibly link me to a site explaining the index laws or something? Because i have no idea what you are referring to. Thanks for the help tho.
$\frac{x^a}{x^b} = x^{a - b}$
and
$\int x^n~dx = \frac{1}{n + 1}x^{n + 1} + C$

-Dan

7. also how does x squared over x to the power of 4 = x squared ?

8. Originally Posted by GreenDay14
also how does x squared over x to the power of 4 = x squared ?
It was a typo.
$\frac{x^2}{x^4} = x^{-2}$

-Dan

9. Originally Posted by GreenDay14
If it is not to much to ask, could you possibly link me to a site explaining the index laws or something? Because i have no idea what you are referring to. Thanks for the help tho.
I'm referring to rules like $a^m a^n = a^{m+n}$, $\frac{a^m}{a^n} = a^{m-n}$, $\frac{1}{a^m} = a^{-m}$, $\sqrt{x} = x^{1/2}$.

You might know them by a different name.

They are pre-calculus things that you're certainly expected to know and use when studying calculus.

10. Thanks for all the help guys.