Mister Exam

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Sum of series:
1/(2n-1)
Identical expressions
one /(2n- one)
1 divide by (2n minus 1)
one divide by (2n minus one)
1/2n-1
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Similar expressions
1/(2n+1)
1/(2*n-1)

Integral of 1/(2n-1) dx

The solution

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 oo           
  /           
 |            
 |     1      
 |  ------- dn
 |  2*n - 1   
 |            
/             
1

$$\int\limits_{1}^{\infty} \frac{1}{2 n - 1}\, dn$$

Integral(1/(2*n - 1), (n, 1, oo))

Detail solution

Let $u = 2 n - 1$ .

Then let $du = 2 dn$ and substitute $\frac{du}{2}$ :

$\int \frac{1}{2 u}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{1}{u}\, du = \frac{\int \frac{1}{u}\, du}{2}$
  1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
  So, the result is: $\frac{\log{\left(u \right)}}{2}$
Now substitute $u$ back in:

$\frac{\log{\left(2 n - 1 \right)}}{2}$
Now simplify:

$\frac{\log{\left(2 n - 1 \right)}}{2}$
Add the constant of integration:

$\frac{\log{\left(2 n - 1 \right)}}{2}+ \mathrm{constant}$

The answer is:

$\frac{\log{\left(2 n - 1 \right)}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                             
 |                              
 |    1             log(2*n - 1)
 | ------- dn = C + ------------
 | 2*n - 1               2      
 |                              
/

$$\int \frac{1}{2 n - 1}\, dn = C + \frac{\log{\left(2 n - 1 \right)}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

oo

$$\infty$$

oo

$$\infty$$

oo

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

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Identical expressions

Similar expressions

Integral of 1/(2n-1) dx

Limits of integration:

The graph:

Piecewise:

The solution