Question

@HELP_ME! f(x)=5/x^3 find the antiderivative

Answer 1

\[\Large\rm f(x)=\frac{5}{x^3}\]If we use an exponent rule, we can write our function like this,\[\Large\rm f(x)=5x^{-3}\]This allows us to more easily apply our power rule.

Answer 2

Errr.. power rule for integration, whatever you want to call it :)

Answer 3

ok so far so good :)

Answer 4

So we're using the fact that the antiderivative of \(\Large\rm x^n\) is \(\Large\rm \frac{1}{n+1}x^{n+1}\)

Answer 5

use

\[\Large \int x^ndx = \frac{1}{n+1}x^{n+1}+C\]

Answer 6

Power increases by 1,
then divide by that new power.

Answer 7

so when the power increases in become -4 right?

Answer 8

Ah! So it's easy to get tripped up when we're dealing with negative numbers.

So our power will become -3+1

Answer 9

ok so its -2 then

Answer 10

Mmm looks good

Answer 11

so.. 5x^-2/-2 +c?

Answer 12

Good good good.
It might be a good idea to put it back into the form that it was given to you in:\[\Large\rm -\frac{5}{2x^{2}}+c\]

Answer 13

correct,

\[\Large -\frac{5}{2}x^{-2} + C\]

Answer 14

Not a big deal though :)

Answer 15

@zepdrix yea my textbook answer puts it back into the form it was given but im glad its still correct lol

Answer 16

thank you both

Answer 17

np