# How to integrate this? #intcolor(white).(3x^2-x+1)/(x^3-x^2)#

By signing up, you agree to our Terms of Service and Privacy Policy

To integrate ( \frac{3x^2 - x + 1}{x^3 - x^2} ), follow these steps:

- Rewrite the fraction as partial fractions if possible.
- Factor the denominator to see if any common factors can be canceled.
- If partial fractions are required, set up the partial fraction decomposition and solve for the unknown constants.
- Integrate each term separately.
- If there are no partial fractions, directly integrate the function.

Since the process can be lengthy and involves several steps, I will provide the result of integrating the given expression:

[ \int \frac{3x^2 - x + 1}{x^3 - x^2} , dx = \ln|x| + 2\ln|x - 1| - \frac{1}{x} + C ]

Where ( C ) is the constant of integration.

By signing up, you agree to our Terms of Service and Privacy Policy

- What is the net area between #f(x) = 2x-5 # and the x-axis over #x in [2, 3 ]#?
- How do you integrate #(8x)/(4x^2+1)#?
- How do you find the definite integral of # (xdx) / ((x^2 + 1)ln(x^2 + 1))# from #[1,2]#?
- How do you evaluate the integral #int 1/(x+x^2)dx# from 1 to #oo#?
- Evaluate the following integral using substitution rule, #int x(2x+5)^8 dx# Online i saw people solving for x too, i dont get that part?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7