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