antiderivatives

[annajee]

Can someone give me some tips on how to find antiderivatives??
I know there are some formulas to use, but for some things
(for example -(x^3/4)), I find it extremely difficult to figure out what was differentiated to get things like that.

Can someone please tell me how people can figure stuff like that out without taking a really really long time to do so?

 

[Deleted member 4993]

Can someone give me some tips on how to find antiderivatives??
I know there are some formulas to use, but for some things
(for example -(x^3/4)), I find it extremely difficult to figure out what was differentiated to get things like that.

Can someone please tell me how people can figure stuff like that out without taking a really really long time to do so?

antiderivative

\(\displaystyle \int x^n \, dx = \frac {1}{n+1}x^{n+1} \, + \, C\)...........you'll just have to remember this like remembering 3+4 = 7

so

\(\displaystyle \int x^{\frac{3}{4}} \, dx \, = \frac {1}{\frac{3}{4}+1}x^{\frac{3}{4}+1} \, + \, C \, = \, \frac {4}{7}x^{\frac{7}{4}} \, + \, C\)

 

[annajee]

Sorry, I think I wrote that example wrong in my question. It was supposed to be like : negative x cubed over 4, so: -(x^3)/4. I'm sorry. So how do you figure out one like that?

 

[mmm4444bot]

... I wrote that example wrong ... It [is] supposed to be ... -(x^3)/4 ...

... how do you figure out one like that?

Hello Anna:

Use the very same method that Subhotosh posted; the only difference is that there is a constant of (-1/4) that you may remove from the integrand.

-(x^3)/4 = (-1/4)*(x^3)

I'll show the constant below using the symbol A.

\(\displaystyle \int A \cdot x^n \, dx \; = \; A \cdot \int x^n \, dx \; = \; \frac {A}{n+1}x^{n+1} \, + \, C\)

Constant factors may always be moved to the outside front of the integral sign.

Cheers,

~ Mark