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Step-by-step Solution

Trigonometric integral $\int\frac{e^{\ln\left(x\right)}\ln\left(x\right)}{x}dx$

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ln
log
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csc

asin
acos
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asinh
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Answer

$x\ln\left(x\right)-x+C_0$

Step-by-step explanation

Problem to solve:

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

Simplifying the logarithm

$\int\frac{x\ln\left(x\right)}{x}dx$
2

Simplifying the fraction by $x$

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

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Answer

$x\ln\left(x\right)-x+C_0$
$\int\frac{\ln\left(x\right)e^{\ln\left(x\right)}}{x}dx$

Main topic:

Integral calculus

Used formulas:

5. See formulas

Time to solve it:

~ 1.35 seconds

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