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The integral of a function times a constant ($4$) is equal to the constant times the integral of the function
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$4\int x^3\ln\left(2x\right)dx$
Learn how to solve problems step by step online. Solve the integral of logarithmic functions int(4x^3ln(2x))dx. The integral of a function times a constant (4) is equal to the constant times the integral of the function. We can solve the integral \int x^3\ln\left(2x\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.