Find the integral $\int\left(x^2-2x+1\right)e^{2x}dx$

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Learn how to solve integrals of exponential functions problems step by step online. Find the integral int((x^2-2x+1)e^(2x))dx. The trinomial \left(x^2-2x+1\right) is a perfect square trinomial, because it's discriminant is equal to zero. Using the perfect square trinomial formula. Factoring the perfect square trinomial. We can solve the integral \int\left(x-1\right)^{2}e^{2x}dx by applying the method of tabular integration by parts, which allows us to perform successive integrations by parts on integrals of the form \int P(x)T(x) dx. P(x) is typically a polynomial function and T(x) is a transcendent function such as \sin(x), \cos(x) and e^x. The first step is to choose functions P(x) and T(x).