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We can solve the integral $\int x\left(-\frac{1}{36}x^2+\frac{2}{9}x-\frac{7}{36}\right)dx$ 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(-1/36x^2+2/9x+-7/36) from 1 to 7. We can solve the integral \int x\left(-\frac{1}{36}x^2+\frac{2}{9}x-\frac{7}{36}\right)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.