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Step-by-step Solution

Solve the trigonometric integral $\int x\ln\left(x^3\right)dx$

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Step-by-step explanation

Problem to solve:

$\int\left(xln\left(x^3\right)\right)dx$

Learn how to solve trigonometric integrals problems step by step online.

$\int3x\ln\left(x\right)dx$

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Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(x*ln(x^3))dx. Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x). The integral of a constant by a function is equal to the constant multiplied by the integral of the function. Use the integration by parts theorem to calculate the integral \int x\ln\left(x\right)dx, using the following formula. First, identify u and calculate du.

Answer

$\frac{1}{4}\left(-\frac{3}{2}x^2+3x^2\ln\left(x\right)\right)+C_0$

Problem Analysis