math question

[theMan]

i need to know the antiderivative of 1/x^n

e.g. : the antiderivative of 1/(x^3).

i know the antiderivative of 1/x = ln |x| but i cant figure out how to find 1/x^n.

please help me.

sincerely,

TheMan with math problems.

 

[cubby1223]

1/(x^n) = (1/x)^n

Not too hard from there.

 

[TheoPetro]

x^-3

antiderive that ish

 

[hypn0tik]

1/x^n = x^(-n)

If you know how to integrate x^n, you can integrate x^(-n)

 

[chuckywang]

Originally posted by: theman
i need to know the antiderivative of 1/x^n

e.g. : the antiderivative of 1/(x^3).

i know the antiderivative of 1/x = ln |x| but i cant figure out how to find 1/x^n.

please help me.

sincerely,

TheMan with math problems.

1/x^n = x^(-n)

Antiderivative of that is 1/(1-n)*x^(1-n), for n not equal to 1.
You already know what it is for n=1.

 

[theMan]

Originally posted by: hypn0tik
1/x^n = x^(-n)

If you know how to integrate x^n, you can integrate x^(-n)

that did it right there. I feel really dumb. Just doing so much math that i can't think properly.

So, 1/x^2 is -1/x and 1/x^3 is -1/2x^2.