Exercise
$\int\frac{3x^3-4x^4+18x-27}{x^4-9x^2}dx$
Step-by-step Solution
Learn how to solve problems step by step online. Find the integral int((3x^3-4x^418x+-27)/(x^4-9x^2))dx. Divide 3x^3-4x^4+18x-27 by x^4-9x^2. Resulting polynomial. Expand the integral \int\left(-4+\frac{3x^{3}-36x^{2}+18x-27}{x^4-9x^2}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int-4dx results in: -4x.
Find the integral int((3x^3-4x^418x+-27)/(x^4-9x^2))dx
Final answer to the exercise
$-4x-2\ln\left|x\right|-\frac{13}{2}\ln\left|x-3\right|+\frac{13}{2}\ln\left|x+3\right|+5\ln\left|\sqrt{x^2-9}\right|+\frac{-3}{x}+C_1$