Integrate the function $\frac{x+1}{x^2-25}$ from 0 to $2$

Learn how to solve definite integrals problems step by step online.

$\int_{0}^{2}\left(\frac{x}{x^2-25}+\frac{1}{x^2-25}\right)dx$

Learn how to solve definite integrals problems step by step online. Integrate the function (x+1)/(x^2-25) from 0 to 2. Expand the fraction \frac{x+1}{x^2-25} into 2 simpler fractions with common denominator x^2-25. Expand the integral \int_{0}^{2}\left(\frac{x}{x^2-25}+\frac{1}{x^2-25}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. Rewrite the fraction \frac{x}{x^2-25} inside the integral as the product of two functions: x\frac{1}{x^2-25}. We can solve the integral \int x\frac{1}{x^2-25}dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula.