$\int_{2}^{\infty }\frac{1}{x^2+x-2}dx$

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$\int\frac{1}{\left(x-1\right)\left(x+2\right)}dx$

Learn how to solve problems step by step online. int(1/(x^2+x+-2))dx&2&infinity. Rewrite the expression \frac{1}{x^2+x-2} inside the integral in factored form. Rewrite the fraction \frac{1}{\left(x-1\right)\left(x+2\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{1}{3\left(x-1\right)}+\frac{-1}{3\left(x+2\right)}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{1}{3\left(x-1\right)}dx results in: \frac{1}{3}\ln\left(x-1\right).