# 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
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lim
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sin
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asin
acos
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sinh
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asinh
acosh
atanh
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asech
acsch

### Videos

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

## 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

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

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