## anonymous 5 years ago whats the anti derivative of 1/(x^3)?? i have an answer but shows its wrong//// help?

1. anonymous

2. anonymous

When doing integrals with a power on the bottom, its often helpful to rewrite it like so anti derivative of x^-3 So lets use the general rule for integration, -3 + 1 = -2 So the anti derivative would be x^(-2) / -2 or in proper form 1 / 2*x^2

3. anonymous

I'm sorry, I mistyped that. The answer is -2 / x^2

4. amistre64

x^-3 -> x^-4/4: 1/(4x^4)

5. anonymous

Wait I keep messing that up.... 1 / -2*x^2

6. amistre64

hah!!... i missed it too lol

7. amistre64

-1/2x^2 is right ;)

8. anonymous

thanks you haha ... so how did you get that>?

9. amistre64

its the reverse of the power rule of a derivative.

10. anonymous

got it .. thanks

11. amistre64

$D(X^n) = n * X^{n-1} \rightarrow D(x^5) = 5x^4$

12. anonymous

you do it correctly you just forgot to include the negative when you divided by the exponent

13. amistre64

$\int\limits_{} X^n dx \rightarrow \frac{X^{n+1}}{n+1}$

14. anonymous

ahh i got it ,.,.,.

15. anonymous

thanks