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Integral of d{x}:
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Integral of log7(x)/log7(e)
Identical expressions
log7(x)/log7(e)
logarithm of 7(x) divide by logarithm of 7(e)
log7x/log7e
log7(x) divide by log7(e)
log7(x)/log7(e)dx

Integral of log7(x)/log7(e) dx

The solution

You have entered [src]

  1                 
  /                 
 |                  
 |      log(x)      
 |  ------------- dx
 |         log(e)   
 |  log(7)*------   
 |         log(7)   
 |                  
/                   
0

$$\int\limits_{0}^{1} \frac{\log{\left(x \right)}}{\frac{\log{\left(e \right)}}{\log{\left(7 \right)}} \log{\left(7 \right)}}\, dx$$

Integral(log(x)/(log(7)*((log(E)/log(7)))), (x, 0, 1))

Detail solution

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

$\int \frac{\log{\left(x \right)}}{\frac{\log{\left(e \right)}}{\log{\left(7 \right)}} \log{\left(7 \right)}}\, dx = \frac{\int \log{\left(x \right)}\, dx}{\log{\left(e \right)}}$
1. Use integration by parts:
  
  $\int \operatorname{u} \operatorname{dv} = \operatorname{u}\operatorname{v} - \int \operatorname{v} \operatorname{du}$
  
  Let $u{\left(x \right)} = \log{\left(x \right)}$ and let $\operatorname{dv}{\left(x \right)} = 1$ .
  
  Then $\operatorname{du}{\left(x \right)} = \frac{1}{x}$ .
  
  To find $v{\left(x \right)}$ :
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int 1\, dx = x$
  Now evaluate the sub-integral.
2. The integral of a constant is the constant times the variable of integration:
  
  $\int 1\, dx = x$
So, the result is: $\frac{x \log{\left(x \right)} - x}{\log{\left(e \right)}}$
Now simplify:

$x \left(\log{\left(x \right)} - 1\right)$
Add the constant of integration:

$x \left(\log{\left(x \right)} - 1\right)+ \mathrm{constant}$

The answer is:

$x \left(\log{\left(x \right)} - 1\right)+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                    
 |                                     
 |     log(x)             -x + x*log(x)
 | ------------- dx = C + -------------
 |        log(e)              log(e)   
 | log(7)*------                       
 |        log(7)                       
 |                                     
/

$$x\,\log x-x$$

Simplify

The answer [src]

-1

$$-1$$

-1

$$-1$$

Упростить

Numerical answer [src]

-1.0

-1.0

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

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Identical expressions

Integral of log7(x)/log7(e) dx

Limits of integration:

The graph:

Piecewise:

The solution