Exercise
$\int\frac{\left(9-4x\right)}{5x^2-4}dx$
Step-by-step Solution
Learn how to solve one-variable linear inequalities problems step by step online. Find the integral int((9-4x)/(5x^2-4))dx. Expand the fraction \frac{9-4x}{5x^2-4} into 2 simpler fractions with common denominator 5x^2-4. Simplify the expression. The integral \int\frac{9}{5x^2-4}dx results in: \frac{-\frac{9}{4}\ln\left(\frac{\sqrt{5}x}{2}+1\right)}{\sqrt{5}}+\frac{\frac{9}{4}\ln\left(\frac{\sqrt{5}x}{2}-1\right)}{\sqrt{5}}. Gather the results of all integrals.
Find the integral int((9-4x)/(5x^2-4))dx
Final answer to the exercise
$\frac{\frac{9}{4}\ln\left|\frac{\sqrt{5}x}{2}-1\right|-\frac{9}{4}\ln\left|\frac{\sqrt{5}x}{2}+1\right|}{\sqrt{5}}-\frac{2}{5}\ln\left|x^2-\frac{4}{5}\right|+C_0$