Mister Exam

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Sum of series:
log(1+1/(n^2))
Identical expressions
log(one + one /(n^ two))
logarithm of (1 plus 1 divide by (n squared ))
logarithm of (one plus one divide by (n to the power of two))
log(1+1/(n2))
log1+1/n2
log(1+1/(n²))
log(1+1/(n to the power of 2))
log1+1/n^2
log(1+1 divide by (n^2))
Similar expressions
log(1-1/(n^2))

Integral of log(1+1/(n^2)) dn

The solution

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 oo               
  /               
 |                
 |     /    1 \   
 |  log|1 + --| dn
 |     |     2|   
 |     \    n /   
 |                
/                 
1

$$\int\limits_{1}^{\infty} \log{\left(1 + \frac{1}{n^{2}} \right)}\, dn$$

Integral(log(1 + 1/(n^2)), (n, 1, oo))

The answer (Indefinite) [src]

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

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

Simplify

The graph

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The answer [src]

pi         
-- - log(2)
2

$$- \log{\left(2 \right)} + \frac{\pi}{2}$$

pi         
-- - log(2)
2

$$- \log{\left(2 \right)} + \frac{\pi}{2}$$

pi/2 - log(2)

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

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Integral of log(1+1/(n^2)) dn

Limits of integration:

The graph:

Piecewise:

The solution