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The integral of a constant times a function is equal to the constant multiplied by the integral of the function
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$\frac{1}{5}\int_{290}^{540}\left(x-3\ln\left(x\right)-\frac{1}{2}e^{-\frac{1}{100}x}\right)dx$
Learn how to solve definite integrals problems step by step online. Integrate the function 1/5(x-3ln(x)-1/2e^(-1/100x)) from 290 to 540. The integral of a constant times a function is equal to the constant multiplied by the integral of the function. Expand the integral \int_{290}^{540}\left(x-3\ln\left(x\right)-\frac{1}{2}e^{-\frac{1}{100}x}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. Solve the product \frac{1}{5}\left(\int_{290}^{540} xdx+\int_{290}^{540}-3\ln\left(x\right)dx+\int_{290}^{540}-\frac{1}{2}e^{-\frac{1}{100}x}dx\right). The integral \frac{1}{5}\int_{290}^{540} xdx results in: 20750.