When finding the anti-derivative of an expression, if it's a fraction, does one have to use the Quotient Rule?

*(We started anti derivatives today in Calc... With a long-term substitute, who is a math major, but not a teacher by degree, at all. Thus, our notes are incomplete, but assignments still due daily!?!)

Specifically, I'm trying to find the anti-derivative of:
"-2/x^3"

Any and all help is greatly appreciated! :)

Question

When finding the anti-derivative of an expression, if it's a fraction, does one have to use the Quotient Rule?

*(We started anti derivatives today in Calc... With a long-term substitute, who is a math major, but not a teacher by degree, at all. Thus, our notes are incomplete, but assignments still due daily!?!)

Specifically, I'm trying to find the anti-derivative of:
"-2/x^3"

Any and all help is greatly appreciated! :)

amonoconnor · Answer

Basically... I know you have to add one to the exponent of a term, then divide by the new exponent, and add C. I know that you address terms individually in polynomials, but this (above) looks like one term to me... So... Do I ignore the top until I divide the bottom? Meh! I am clueless!

ganeshie8 · Answer

rewrite $\large \frac{-2}{x^3}$ as $-2x^{-3}$

amonoconnor · Answer

And then proceed, well, normally?

ganeshie8 · Answer

yes, then use below :

$\large  \int x^n = \frac{x^{n+1}}{n+1} + c$

amonoconnor · Answer

This guy teaching Calc to us told me to "not change the sign of the exponents in the problem by rearranging". Is that valid?

isaiah.feynman · Answer

Well @amonoconnor you integrate the function. Use the form @ganeshie8 showed

isaiah.feynman · Answer

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