Final answer to the problem
Step-by-step Solution
Specify the solving method
Find the integral
Learn how to solve integrals of rational functions problems step by step online.
$\int\frac{x+3}{x-5}dx$
Learn how to solve integrals of rational functions problems step by step online. Simplify the expression f(x)=(x+3)/(x-5). Find the integral. Expand the fraction \frac{x+3}{x-5} into 2 simpler fractions with common denominator x-5. Expand the integral \int\left(\frac{x}{x-5}+\frac{3}{x-5}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. We can solve the integral \int\frac{x}{x-5}dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that x-5 it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.