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We can solve the integral $\int\left(x^4-4x^2+9\right)e^{-\frac{1}{2}x}dx$ by applying integration by parts method to calculate the integral of the product of two functions, using the following formula
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$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$
Learn how to solve definite integrals problems step by step online. Integrate the function (x^4-4x^2+9)e^(-1/2x) from 0 to 1. We can solve the integral \int\left(x^4-4x^2+9\right)e^{-\frac{1}{2}x}dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify u and calculate du. Now, identify dv and calculate v. Solve the integral.