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Since the integral $\int_{0}^{2}\frac{1}{\left(x-1\right)^2}dx$ has a discontinuity inside the interval, we have to split it in two integrals
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$\int_{0}^{1}\frac{1}{\left(x-1\right)^2}dx+\int_{1}^{2}\frac{1}{\left(x-1\right)^2}dx$
Learn how to solve definite integrals problems step by step online. Integrate the function 1/((x-1)^2) from 0 to 2. Since the integral \int_{0}^{2}\frac{1}{\left(x-1\right)^2}dx has a discontinuity inside the interval, we have to split it in two integrals. The integral \int_{0}^{1}\frac{1}{\left(x-1\right)^2}dx results in: \lim_{c\to1}\left(\frac{1}{-c+1}-1\right). The integral \int_{1}^{2}\frac{1}{\left(x-1\right)^2}dx results in: \lim_{c\to1}\left(-1+\frac{-1}{-c+1}\right). Gather the results of all integrals.