Exercise
$\int_3^{\infty}\left(\frac{8}{x^2-x}\right)dx$
Step-by-step Solution
Learn how to solve integrals of exponential functions problems step by step online. Integrate the function 8/(x^2-x) from 3 to infinity. Rewrite the expression \frac{8}{x^2-x} inside the integral in factored form. Rewrite the fraction \frac{8}{x\left(x-1\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{-8}{x}+\frac{8}{x-1}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{-8}{x}dx results in: -8\ln\left(x\right).
Integrate the function 8/(x^2-x) from 3 to infinity
Final answer to the exercise
The integral diverges.