Exercise
$\int\frac{1}{x\left(x^4-4\right)}dx$
Step-by-step Solution
Learn how to solve differential equations problems step by step online. Find the integral int(1/(x(x^4-4)))dx. Rewrite the expression \frac{1}{x\left(x^4-4\right)} inside the integral in factored form. Take the constant \frac{1}{-1} out of the integral. Rewrite the fraction \frac{1}{x\left(2+x^2\right)\left(\sqrt[4]{4}+x\right)\left(\sqrt[4]{4}-x\right)} in 4 simpler fractions using partial fraction decomposition. Simplify the expression.
Find the integral int(1/(x(x^4-4)))dx
Final answer to the exercise
$-\frac{1}{4}\ln\left|x\right|+\frac{1}{8}\ln\left|\sqrt{2+x^2}\right|+\frac{1}{16}\ln\left|x+\sqrt[4]{4}\right|+\frac{1}{16}\ln\left|\sqrt[4]{4}-x\right|+C_1$