Exercise
$\int\frac{x^2+2x-3}{x^3+x^2-2x}dx$
Step-by-step Solution
Learn how to solve problems step by step online. Find the integral int((x^2+2x+-3)/(x^3+x^2-2x))dx. Rewrite the expression \frac{x^2+2x-3}{x^3+x^2-2x} inside the integral in factored form. Factor the trinomial x^2+2x-3 finding two numbers that multiply to form -3 and added form 2. Rewrite the polynomial as the product of two binomials consisting of the sum of the variable and the found values. Simplifying.
Find the integral int((x^2+2x+-3)/(x^3+x^2-2x))dx
Final answer to the exercise
$\frac{3}{2}\ln\left|x\right|-\frac{1}{2}\ln\left|x+2\right|+C_0$