Exercise
$\int\left(\frac{1}{\left(x+5\right)^{-1}}+x^{-\frac{2}{3}}-\frac{x}{1+x^2}\right)dx$
Step-by-step Solution
Learn how to solve differential equations problems step by step online. Find the integral int(1/((x+5)^(-1))+x^(-2/3)(-x)/(1+x^2))dx. Simplify the expression. The integral \int xdx results in: \frac{1}{2}x^2. The integral \int5dx results in: 5x. The integral \int x^{-\frac{2}{3}}dx results in: 3\sqrt[3]{x}.
Find the integral int(1/((x+5)^(-1))+x^(-2/3)(-x)/(1+x^2))dx
Final answer to the exercise
$\frac{1}{2}x^2+5x+3\sqrt[3]{x}-\frac{1}{2}\ln\left|1+x^2\right|+C_0$