Question

Find the most general anti-derivative of the function below..

Answer 1

whats the function?

Answer 2

\[\frac{3 - 6x^3 + 2x^6}{x^6}\]

Answer 3

start by dividing each term by
\[x^6\] then use the power rule backwards

Answer 4

\[3x^{-6} - 6x^{-3} + 2\]

Answer 5

then power rule backwards?

Answer 6

\[\int(\frac{3}{x^6}-\frac{6}{x^3}+2)dx\]

Answer 7

cant use it forwards lol

Answer 8

well at this point you can create 3 separate integrals

Answer 9

\[\int x^n dx=\frac{x^{n+1}}{n+1}\]

Answer 10

and bring the constants out in front

Answer 11

in other words add one to the exponent and divide by the result.

Answer 12

so for example
\[\int\frac{3}{x^6}dx=-\frac{3}{5x^5}\]

Answer 13

if u don't understand what satelllite is saying be extremely concerned at this point

Answer 14

I do understand what he is saying.

Answer 15

\[-\frac{3}{5}x^{-5} + 3x^{-2} + C\] is that correct?