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We can solve the integral $\int x\left(25-x^2\right)dx$ 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 problems step by step online. Integrate the function x(25-x^2) from 0 to 5. We can solve the integral \int x\left(25-x^2\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.