Integral of log(2)x dx

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 1/2           
  /            
 |             
 |  log(2)*x dx
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/              
1/4

$$\int\limits_{\frac{1}{4}}^{\frac{1}{2}} x \log{\left(2 \right)}\, dx$$

Simplify

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int x \log{\left(2 \right)}\, dx = \log{\left(2 \right)} \int x\, dx$
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x\, dx = \frac{x^{2}}{2}$
So, the result is: $\frac{x^{2} \log{\left(2 \right)}}{2}$
Add the constant of integration:

$\frac{x^{2} \log{\left(2 \right)}}{2}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \log{\left(2 \right)}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                   2       
 |                   x *log(2)
 | log(2)*x dx = C + ---------
 |                       2    
/

$${{\log 2\,x^2}\over{2}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

3*log(2)
--------
   32

$${{3\,\log 2}\over{32}}$$

3*log(2)
--------
   32

$$\frac{3 \log{\left(2 \right)}}{32}$$

Simplify

Numerical answer [src]

0.0649825481774949

0.0649825481774949

The graph

Use the examples entering the upper and lower limits of integration.