Exercise
$\int\frac{5x+4}{x^3-4x^2-21x}dx$
Step-by-step Solution
Learn how to solve problems step by step online. Find the integral int((5x+4)/(x^3-4x^2-21x))dx. Rewrite the expression \frac{5x+4}{x^3-4x^2-21x} inside the integral in factored form. Rewrite the fraction \frac{5x+4}{x\left(x-7\right)\left(x+3\right)} in 3 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{-4}{21x}+\frac{39}{70\left(x-7\right)}+\frac{-11}{30\left(x+3\right)}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{-4}{21x}dx results in: -\frac{4}{21}\ln\left(x\right).
Find the integral int((5x+4)/(x^3-4x^2-21x))dx
Final answer to the exercise
$-\frac{4}{21}\ln\left|x\right|+\frac{39}{70}\ln\left|x-7\right|-\frac{11}{30}\ln\left|x+3\right|+C_0$