Exercise
$\int x\cdot\left(x+2\right)^{-2}dx$
Step-by-step Solution
Learn how to solve integrals by partial fraction expansion problems step by step online. Find the integral int(x(x+2)^(-2))dx. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number. Multiplying the fraction by x. Rewrite the fraction \frac{x}{\left(x+2\right)^{2}} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{1}{x+2}+\frac{-2}{\left(x+2\right)^{2}}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately.
Find the integral int(x(x+2)^(-2))dx
Final answer to the exercise
$\ln\left|x+2\right|+\frac{2}{x+2}+C_0$