Exercise
$\int\frac{x^4-x^3+x+1}{\left(x^3-x^2\right)}dx$
Step-by-step Solution
Learn how to solve trigonometric integrals problems step by step online. Find the integral int((x^4-x^3x+1)/(x^3-x^2))dx. Divide x^4-x^3+x+1 by x^3-x^2. Resulting polynomial. Expand the integral \int\left(x+\frac{x+1}{x^3-x^2}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int xdx results in: \frac{1}{2}x^2.
Find the integral int((x^4-x^3x+1)/(x^3-x^2))dx
Final answer to the exercise
$\frac{1}{2}x^2-2\ln\left|x\right|+2\ln\left|x-1\right|+\frac{1}{x}+C_0$