Exercise
$\int\:\frac{5x^3-122x-5}{x^2-25}dx$
Step-by-step Solution
Learn how to solve problems step by step online. Find the integral int((5x^3-122x+-5)/(x^2-25))dx. Divide 5x^3-122x-5 by x^2-25. Resulting polynomial. Expand the integral \int\left(5x+\frac{3x-5}{x^2-25}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int5xdx results in: \frac{5}{2}x^2.
Find the integral int((5x^3-122x+-5)/(x^2-25))dx
Final answer to the exercise
$\frac{5}{2}x^2+\frac{1}{2}\ln\left|x+5\right|-\frac{1}{2}\ln\left|x-5\right|+3\ln\left|\sqrt{x^2-25}\right|+C_1$