Learn how to solve problems step by step online. Find the integral int(1/((x-1)(x^2-16)))dx. Rewrite the expression \frac{1}{\left(x-1\right)\left(x^2-16\right)} inside the integral in factored form. Rewrite the fraction \frac{1}{\left(x-1\right)\left(x+4\right)\left(x-4\right)} in 3 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{-1}{15\left(x-1\right)}+\frac{1}{40\left(x+4\right)}+\frac{1}{24\left(x-4\right)}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{-1}{15\left(x-1\right)}dx results in: -\frac{1}{15}\ln\left(x-1\right).

Find the integral int(1/((x-1)(x^2-16)))dx