Indefinate Integral

[CatchThis2]

Evaluate:

(7/x^4) -(4/x^6)+12

So far I brought the 7 out front and simplified x^4 as x^5/5

Next I brought the 4 out front and simplified x^6 as x^7/7

Next 12 = 12x

From there I am stuck

 

[lookagain]

Evaluate:

(7/x^4) -(4/x^6)+12

So far I brought the 7 out front and simplified x^4 as x^5/5

Next I brought the 4 out front and simplified x^6 as x^7/7

Next 12 = 12x

From there I am stuck

If you had had \(\displaystyle 7x^4 - 4x^6 + 12,\) then the indefinite integral would have been

\(\displaystyle 7\bigg({\frac{x^5}{5}\bigg) - 4\bigg(\frac{x^7}{7}\bigg) + 12x + \bigg C \ =\)

\(\displaystyle \frac{7}{5}x^5 - \frac{4}{7}x^7 + 12x + \bigg C \ \ or\)

\(\displaystyle \frac{7x^5}{5} - \frac{4x^7}{7} + 12x + \bigg C\)


However, you have the equivalent of \(\displaystyle 7x^{-4} - 4x^{-6} + 12.\)

Then, the indefinite integral is

\(\displaystyle \frac{7}{-3}x^{-3} - \frac{4}{-5}x^{-5} + 12x + \bigg C \ =\)

\(\displaystyle \frac{-7}{3x^3} - \frac{-4}{5x^5} + 12x + \bigg C\ =\)

\(\displaystyle \frac{-7}{3x^3} + \frac{4}{5x^5} + 12x + \bigg C\)