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Step-by-step Solution

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

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e
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ln
log
log
lim
d/dx
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sin
cos
tan
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csc

asin
acos
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asinh
acosh
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Answer

$x^2\left(-\frac{3}{8}+\frac{3}{4}\ln\left(x\right)\right)+C_0$

Step-by-step explanation

Problem to solve:

$\int\left(x\ln x^3\right)dx$
1

Using the power rule of logarithms: $\log_a(x^n)=n\cdot\log_a(x)$

$\int3x\ln\left(x\right)dx$
2

The integral of a constant by a function is equal to the constant multiplied by the integral of the function

$3\int x\ln\left(x\right)dx$

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Answer

$x^2\left(-\frac{3}{8}+\frac{3}{4}\ln\left(x\right)\right)+C_0$