Question

Evaluate the integral
(8/x-1/x^5+1/3x^7) dx

Answer 1

Is that \[\int\limits (\frac{ 8 }{ x } - \frac{ 1 }{ x } + \frac{ 1 }{ 3 }x^7) dx\]?

Answer 2

^meant to write \[\int\limits\limits (\frac{ 8 }{ x } - \frac{ 1 }{ x ^5} + \frac{ 1 }{ 3 }x^7) dx\]

Answer 3

\[1/3x ^{7}\]

Answer 4

everything else is right

Answer 5

Ok, so you can split this off into multiple integrals like:\[8 \int\limits (\frac{ 1 }{ x }) dx - \int\limits (\frac{ 1 }{ x^5 }) dx + \frac{ 1 }{ 3 } \int\limits (\frac{ 1 }{ x^7 }) dx\] Do you understand what I did there and how to go from there?

Answer 6

how do I handle the 1/x^5

Answer 7

You can treat that as \[x ^{-5}\] and just apply the power rule