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\int\frac{\ln\left(x\right)}{x^3}dx

Integral of (ln(x))/(x^3)

Answer

$\frac{1}{121}\int\frac{\ln\left(t\right)}{\sqrt[11]{t^{13}}}dt$

Step-by-step explanation

Problem

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

Solve the integral $\int\frac{\ln\left(x\right)}{x^3}dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=x^3 \\ du=3x^{2}dx\end{matrix}$

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Answer

$\frac{1}{121}\int\frac{\ln\left(t\right)}{\sqrt[11]{t^{13}}}dt$

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$\int\frac{\ln\left(x\right)}{x^3}dx$

Main topic:

Integration by substitution

Used formulas:

1. See formulas

Time to solve it:

1.74 seconds