Exercise
$\int\frac{x^4-2x^2+3x+4}{x^4-x^2-2x+2}dx$
Step-by-step Solution
Learn how to solve problems step by step online. Find the integral int((x^4-2x^23x+4)/(x^4-x^2-2x+2))dx. Divide x^4-2x^2+3x+4 by x^4-x^2-2x+2. Resulting polynomial. Expand the integral \int\left(1+\frac{-x^{2}+5x+2}{x^4-x^2-2x+2}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int1dx results in: x.
Find the integral int((x^4-2x^23x+4)/(x^4-x^2-2x+2))dx
Final answer to the exercise
$x-\frac{9}{25}\ln\left|x-1\right|+\frac{-6}{5\left(x-1\right)}-\frac{37}{25}\arctan\left(x+1\right)+\frac{9}{50}\ln\left|\left(x+1\right)^2+1\right|+C_0$