Trouble with the integral Help

[depecheSoul]

Trouble with the integral! Help

While I was working some examples of integrals from book, I found this example:

$\int {{x^3-1}\over{4x^3+x}}$
and I can not solve it, because I get always incorrect result.

Result is: (from book)

${x \over 4}+{{x \over 16}*{ln ({{x^{16}}\over{(2x-1)^7(2x+1)^9}}})}$

Can you help me solve it!

Thanks.

 

[gb7nash]

Before you do anything with the integral, take polynomial long division, since the degree of the numerator >= degree of the denominator.

 

[Ksitov]

While I was working some examples of integrals from book, I found this example:

$\int {{x^3-1}\over{4x^3+x}}$
and I can not solve it, because I get always incorrect result.

Result is: (from book)

${x \over 4}+{{x \over 16}*{ln ({{x^{16}}\over{(2x-1)^7(2x+1)^9}}})}$

Can you help me solve it!

Thanks.

You can notice x^3 - 1 is of the form "a^3-b^3". You can factorize ;) !

And you can factorize: 4x^3 + x.

It is a partial fraction.

Good luck ;) !

 

[depecheSoul]

Thank you!