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Step-by-step Solution
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We could not solve this problem by using the method: Integrate by parts
Expand the integral $\int\left(x+\frac{-x-1}{x^2\left(x-1\right)}\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately
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$\int xdx+\int\frac{-x-1}{x^2\left(x-1\right)}dx$
Learn how to solve integral calculus problems step by step online. Integrate int(x+(-x-1)/(x^2(x-1)))dx. Expand the integral \int\left(x+\frac{-x-1}{x^2\left(x-1\right)}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int xdx results in: \frac{1}{2}x^2. The integral \int\frac{-x-1}{x^2\left(x-1\right)}dx results in: \frac{1}{-x}-2\ln\left(x-1\right)+2\ln\left(x\right). Gather the results of all integrals.