anonymous
  • anonymous
integral((x^3+x+1)/(x^4+x^2+1))
Mathematics
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
jamiebookeater
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

anonymous
  • anonymous
http://www.wolframalpha.com/input/?i=integral%28%28x^3%2Bx%2B1%29%2F%28x^4%2Bx^2%2B1%29%29
anonymous
  • anonymous
I am concerned with what substitution has to be carried out and not the answer
anonymous
  • anonymous
you have the form P(x)/Q(x) where P and Q are polynomials. Further the degree of the numerator, namely 3, is one less than the denominator. In such situations, find \[dQ/dx \] and express P in terms of that. \[\int\limits{dy/y} = \log y\] the remaining terms are hopefully simpler. If you need more help ask

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
\[d/dx ({{x^4+x^2+1}}) = 4x^3 + 2x \] so \[P(x) = {1/4}({dQ/dx}) + (1/2)x + 1 \] So the original problem reduces to integrating \[dQ/Q + (1/2)\int\limits x dx/Q + \int\limits dx/Q \]
anonymous
  • anonymous
Sorry the last equation should read: \[(1/4)\int\limits dQ/Q + (1/2)\int\limits\limits x dx/Q + \int\limits\limits dx/Q\]

Looking for something else?

Not the answer you are looking for? Search for more explanations.