[tex]integration \: of \frac{1}{2} ln(2x {^{2}

Ответ:

tsimonej12

10.03.2022

Using properties of the logarithm, you can rearrange the integrand as

$\dfrac12\ln(2x^2)=\dfrac{\ln2+\ln x^2}2=\dfrac{\ln2+2\ln x}2=\ln\sqrt2+\ln x$

Then recall that the integral of $\ln x$ is

$\displaystyle\int\ln x\,\mathrm dx=x(\ln x-1)+C$

(or you can find that out by integrating by parts) and so

$\displaystyle\int\frac12\ln(2x^2)\,\mathrm dx=(\ln\sqrt2)x+x(\ln x-1)+C$

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ngj312

20.10.2022

A reflection is a transformation that acts like a mirror: It swaps all pairs of points that are on exactly opposite sides of the line of reflection.

The line of reflection can be defined by an equation or by two points it passes through.

Step-by-step explanation:

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