Exercise
$\int\frac{x+4}{x^{3}-16x}dx$
Step-by-step Solution
Learn how to solve addition of numbers problems step by step online. Find the integral int((x+4)/(x^3-16x))dx. Rewrite the expression \frac{x+4}{x^3-16x} inside the integral in factored form. Rewrite the fraction \frac{1}{x\left(x-4\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{-1}{4x}+\frac{1}{4\left(x-4\right)}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{-1}{4x}dx results in: -\frac{1}{4}\ln\left(x\right).
Find the integral int((x+4)/(x^3-16x))dx
Final answer to the exercise
$-\frac{1}{4}\ln\left|x\right|+\frac{1}{4}\ln\left|x-4\right|+C_0$