Calculating the Integral of a Rational Function

[electronic engineer]

how to calculate the calculus of this rational function:

\int \frac{dx}{{x+x^6}}

could anyone get me through the solution?!

 

[TD]

Hint:

\frac{1}{{x + x^6 }} = \frac{1}{{x\left( {1 + x^5 } \right)}} = \frac{{\frac{1}{{x^6 }}}}{{\frac{{1 + x^5 }}{{x^5 }}}} = \frac{{\frac{1}{{x^6 }}}}{{\frac{1}{{x^5 }} + 1}}

 

[electronic engineer]

so final result:

-0.2* ln(1+x^-5)


is that right?

 

[benorin]

yep: need to check an integral, use www.integrals.com

 

[TD]

so final result:

-0.2* ln(1+x^-5)


is that right?

Indeed, if you don't forget the constant of integration