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Identical expressions
five ^ln(x- seven)/(x- seven)
5 to the power of ln(x minus 7) divide by (x minus 7)
five to the power of ln(x minus seven) divide by (x minus seven)
5ln(x-7)/(x-7)
5lnx-7/x-7
5^lnx-7/x-7
5^ln(x-7) divide by (x-7)
5^ln(x-7)/(x-7)dx
Similar expressions
5^ln(x-7)/(x+7)
5^ln(x+7)/(x-7)

Integral of 5^ln(x-7)/(x-7) dx

The solution

You have entered [src]

  1               
  /               
 |                
 |   log(x - 7)   
 |  5             
 |  ----------- dx
 |     x - 7      
 |                
/                 
0

$$\int\limits_{0}^{1} \frac{5^{\log{\left(x - 7 \right)}}}{x - 7}\, dx$$

Integral(5^log(x - 7)/(x - 7), (x, 0, 1))

Detail solution

There are multiple ways to do this integral.
Method #1
1. Let $u = \log{\left(x - 7 \right)}$ .
  
  Then let $du = \frac{dx}{x - 7}$ and substitute $du$ :
  
  $\int 5^{u}\, du$
  1. The integral of an exponential function is itself divided by the natural logarithm of the base.
    
    $\int 5^{u}\, du = \frac{5^{u}}{\log{\left(5 \right)}}$
  Now substitute $u$ back in:
  
  $\frac{5^{\log{\left(x - 7 \right)}}}{\log{\left(5 \right)}}$
Method #2
1. Let $u = x - 7$ .
  
  Then let $du = dx$ and substitute $du$ :
  
  $\int \frac{5^{\log{\left(u \right)}}}{u}\, du$
  1. Let $u = \log{\left(u \right)}$ .
    
    Then let $du = \frac{du}{u}$ and substitute $du$ :
    
    $\int 5^{u}\, du$
    1. The integral of an exponential function is itself divided by the natural logarithm of the base.
      
      $\int 5^{u}\, du = \frac{5^{u}}{\log{\left(5 \right)}}$
    Now substitute $u$ back in:
    
    $\frac{5^{\log{\left(u \right)}}}{\log{\left(5 \right)}}$
  Now substitute $u$ back in:
  
  $\frac{5^{\log{\left(x - 7 \right)}}}{\log{\left(5 \right)}}$
Now simplify:

$\frac{5^{\log{\left(x - 7 \right)}}}{\log{\left(5 \right)}}$
Add the constant of integration:

$\frac{5^{\log{\left(x - 7 \right)}}}{\log{\left(5 \right)}}+ \mathrm{constant}$

The answer is:

$\frac{5^{\log{\left(x - 7 \right)}}}{\log{\left(5 \right)}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                
 |                                 
 |  log(x - 7)           log(x - 7)
 | 5                    5          
 | ----------- dx = C + -----------
 |    x - 7                log(5)  
 |                                 
/

$$\int \frac{5^{\log{\left(x - 7 \right)}}}{x - 7}\, dx = \frac{5^{\log{\left(x - 7 \right)}}}{\log{\left(5 \right)}} + C$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

 pi*I + log(6)    pi*I + log(7)
5                5             
-------------- - --------------
    log(5)           log(5)

$$\frac{5^{\log{\left(6 \right)} + i \pi}}{\log{\left(5 \right)}} - \frac{5^{\log{\left(7 \right)} + i \pi}}{\log{\left(5 \right)}}$$

 pi*I + log(6)    pi*I + log(7)
5                5             
-------------- - --------------
    log(5)           log(5)

$$\frac{5^{\log{\left(6 \right)} + i \pi}}{\log{\left(5 \right)}} - \frac{5^{\log{\left(7 \right)} + i \pi}}{\log{\left(5 \right)}}$$

5^(pi*i + log(6))/log(5) - 5^(pi*i + log(7))/log(5)

Numerical answer [src]

(-1.05449837299643 + 2.94529018117065j)

(-1.05449837299643 + 2.94529018117065j)

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

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Identical expressions

Similar expressions

Integral of 5^ln(x-7)/(x-7) dx

Limits of integration:

The graph:

Piecewise:

The solution

Method #1

Method #2