Final answer to the problem
$\frac{10}{7}\ln\left|x+3\right|-\frac{3}{7}\ln\left|x-4\right|+C_0$
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Step-by-step Solution
Learn how to solve integrals by partial fraction expansion problems step by step online. Find the integral int((x-7)/((x+3)(x-4)))dx. Rewrite the fraction \frac{x-7}{\left(x+3\right)\left(x-4\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{10}{7\left(x+3\right)}+\frac{-3}{7\left(x-4\right)}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{10}{7\left(x+3\right)}dx results in: \frac{10}{7}\ln\left(x+3\right). The integral \int\frac{-3}{7\left(x-4\right)}dx results in: -\frac{3}{7}\ln\left(x-4\right).
Final answer to the problem
$\frac{10}{7}\ln\left|x+3\right|-\frac{3}{7}\ln\left|x-4\right|+C_0$
