Finding the antiderivative of 1/x³

[discy]

how to compute the ANTI derivative of 1 / x^3
I think I need the formula: f(x) = 1/x^n than f'(x) = -n/x^n+1 but I'm not sure and don't know how to use it.

I know the answer is: -0.5 * x^-2 but have no idea why.

could someone explain this to me please?

 

[LCKurtz]

The familiar antiderivative formula

$$\int x^n\, dx = \frac{x^{n+1}}{n+1}+C$$

also works for negative exponents. Write your fraction as a negative exponent.

 

[discy]

The familiar antiderivative formula

$$\int x^n\, dx = \frac{x^{n+1}}{n+1}+C$$

also works for negative exponents. Write your fraction as a negative exponent.

thanks for your answer.

now how would I put 1/x³ into that formula to get -0.5 * x^-2 ?

 

[LCKurtz]

thanks for your answer.

now how would I put 1/x³ into that formula to get -0.5 * x^-2 ?

Write 1/x³ as xⁿ using a negative exponent and use the formua.

 

[discy]

hm okay. like x^-3. got it.

I guess I should learn this formula, not only because it's a "familiar" one for you guys. But also because for some reason it's not on my formula sheet.

:) tnx for your help.

 

[SteamKing]

You probably should throw that formula sheet away and download a more complete listing of integral formulas.

Link: http://en.wikipedia.org/wiki/Lists_of_integrals