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Using the power rule of logarithms: $\log_a(x^n)=n\cdot\log_a(x)$
Learn how to solve definite integrals problems step by step online.
$\int_{1}^{5}3\sqrt{2x}\log \left(x\right)dx$
Learn how to solve definite integrals problems step by step online. Integrate the function (2x)^1/2log(x^3) from 1 to 5. Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x). The integral of a constant times a function is equal to the constant multiplied by the integral of the function. Change the logarithm to base e applying the change of base formula for logarithms: \log_b(a)=\frac{\log_x(a)}{\log_x(b)}. Simplify the expression inside the integral.