Mister Exam

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Identical expressions
dz/(z- five)
dz divide by (z minus 5)
dz divide by (z minus five)
dz/z-5
dz divide by (z-5)
Similar expressions
dz/(z+5)

Integral of dz/(z-5) dx

The solution

You have entered [src]

 pi           
  /           
 |            
 |      1     
 |  1*----- dz
 |    z - 5   
 |            
/             
I

$$\int\limits_{i}^{\pi} 1 \cdot \frac{1}{z - 5}\, dz$$

Integral(1/(z - 1*5), (z, i, pi))

Detail solution

Let $u = z - 5$ .

Then let $du = dz$ and substitute $du$ :

$\int \frac{1}{u}\, du$
1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
Now substitute $u$ back in:

$\log{\left(z - 5 \right)}$
Now simplify:

$\log{\left(z - 5 \right)}$
Add the constant of integration:

$\log{\left(z - 5 \right)}+ \mathrm{constant}$

The answer is:

$\log{\left(z - 5 \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                           
 |                            
 |     1                      
 | 1*----- dz = C + log(z - 5)
 |   z - 5                    
 |                            
/

$$\int 1 \cdot \frac{1}{z - 5}\, dz = C + \log{\left(z - 5 \right)}$$

Simplify

The answer [src]

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

$$\log{\left(5 - \pi \right)} - \log{\left(-5 + i \right)} + i \pi$$

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

$$\log{\left(5 - \pi \right)} - \log{\left(-5 + i \right)} + i \pi$$

Упростить

Numerical answer [src]

(-1.00932841346108 + 0.197395559849881j)

(-1.00932841346108 + 0.197395559849881j)

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

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Identical expressions

Similar expressions

Integral of dz/(z-5) dx

Limits of integration:

The graph:

Piecewise:

The solution