Question

integration of log2x

Answer 1

Answer:

xlog(2x)−x+C

Step-by-step explanation:

log(2x)

Solution:-

∫log(2x)

Now integrating by parts

log(2x).(x)−∫12x.(2)(x)dx

xlog(2x)−∫2x2xdx

xlog(2x)−∫dx

xlog(2x)−x+C

Answer 2

$\displaystyle \sf{ \int \: log \: 2x \: dx = xlog \: 2x- x + c}$

Given :

$\displaystyle \sf{ \int \: log \: 2x \: dx }$

To find :

The value of the integral

Solution :

Step 1 of 2 :

Write down the given Integral

Here the given Integral is

$\displaystyle \sf{ \int \: log \: 2x \: dx }$

Step 2 of 2 :

Integrate the integral

We integrate by parts as below

$\displaystyle \sf{ \int \: log \: 2x \: dx }$

$\displaystyle \sf{ = \int \: log \: 2x \: .1 \: dx }$

$\displaystyle \sf{ = log \: 2x \int 1 \: dx - \int \bigg[ \frac{d}{dx} (log \: 2x) \int 1 \: dx\bigg]dx}$

$\displaystyle \sf{ = (log \: 2x) .x - \int \frac{2}{2x} .x \: dx}$

$\displaystyle \sf{ = xlog \: 2x- \int 1 \: dx}$

$\displaystyle \sf{ = xlog \: 2x- x + c}$

Where c is integration constant

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