Posted by **john** on Sunday, March 7, 2010 at 4:39pm.

evaluate the integral:

(x^3)/((x^2)+1)

- calculus -
**MathMate**, Sunday, March 7, 2010 at 7:43pm
For rational functions, first step is to see if the degree of the numerator is higher than that of the denominator. If this is the case (as in the present problem), do a long division to reduce the numerator to a degree lower than that of the denominator.

Thus:

(x^3)/((x^2)+1)

=x - x/((x^2)+1)

=x - (1/2)(2x)/(x²+1)

the first term can be integrated using the simple power rule.

We note that the second term has been transformed into the form where the numerator is the derivative of the denominator. The integral of the second term is thus -(1/2)ln(denominator).

Post if more help is required.

## Answer this Question

## Related Questions

- Calculus - Evaluate the integral: 16csc(x) dx from pi/2 to pi (and determine if ...
- Calculus 2 - The question is: Evaluate the improper integral for a>0. The ...
- Calculus - evaluate the integral or state that it diverges. Check if I did it ...
- Calculus II/III - A. Find the integral of the following function. Integral of (x...
- Calculus integral - evaluate the integral: integral from -pi/4 to 0 for the ...
- calculus - evaluate integral or state that it is diverges integral -oo, -2 [2/(x...
- Calculus - integral -oo, oo [(2x)/(x^2+1)^2] dx (a) state why the integral is ...
- Calculus - for the function F(t)=ln(t^2), let f(t)=F'(t). Write the integral ...
- calculus - consider the function f(x) = e^x(sinNx) on the interval [0,1] where N...
- calculus - consider the function f(x) = e^x(sinNx) on the interval [0,1] where N...