Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of x^2*e^(x^3)
Integral of x^2/(x^2+1)^4
Integral of sin(2x)^2
Integral of sqrt(1+e^(2x))
Identical expressions
four /(x(ln^2x+ one))
4 divide by (x(ln squared x plus 1))
four divide by (x(ln squared x plus one))
4/(x(ln2x+1))
4/xln2x+1
4/(x(ln²x+1))
4/(x(ln to the power of 2x+1))
4/xln^2x+1
4 divide by (x(ln^2x+1))
4/(x(ln^2x+1))dx
Similar expressions
4/(x(ln^2x-1))

Integral of 4/(x(ln^2x+1)) dx

The solution

You have entered [src]

 oo                   
  /                   
 |                    
 |         4          
 |  --------------- dx
 |    /   2       \   
 |  x*\log (x) + 1/   
 |                    
/                     
1

\int\limits_{1}^{\infty} \frac{4}{x \left(\log{\left(x \right)}^{2} + 1\right)}\, dx

Integral(4/((x*(log(x)^2 + 1))), (x, 1, oo))

Detail solution

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

$\int \frac{4}{x \left(\log{\left(x \right)}^{2} + 1\right)}\, dx = 4 \int \frac{1}{x \left(\log{\left(x \right)}^{2} + 1\right)}\, dx$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $\operatorname{RootSum} {\left(4 z^{2} + 1, \left( i \mapsto i \log{\left(2 i + \log{\left(x \right)} \right)} \right)\right)}$
So, the result is: $4 \operatorname{RootSum} {\left(4 z^{2} + 1, \left( i \mapsto i \log{\left(2 i + \log{\left(x \right)} \right)} \right)\right)}$
Now simplify:

$- 2 i \log{\left(\log{\left(x \right)} - i \right)} + 2 i \log{\left(\log{\left(x \right)} + i \right)}$
Add the constant of integration:

$- 2 i \log{\left(\log{\left(x \right)} - i \right)} + 2 i \log{\left(\log{\left(x \right)} + i \right)}+ \mathrm{constant}$

The answer is:

- 2 i \log{\left(\log{\left(x \right)} - i \right)} + 2 i \log{\left(\log{\left(x \right)} + i \right)}+ \mathrm{constant}

The answer (Indefinite) [src]

  /                                                                      
 |                                                                       
 |        4                          /   2                              \
 | --------------- dx = C + 4*RootSum\4*z  + 1, i -> i*log(2*i + log(x))/
 |   /   2       \                                                       
 | x*\log (x) + 1/                                                       
 |                                                                       
/

\int \frac{4}{x \left(\log{\left(x \right)}^{2} + 1\right)}\, dx = C + 4 \operatorname{RootSum} {\left(4 z^{2} + 1, \left( i \mapsto i \log{\left(2 i + \log{\left(x \right)} \right)} \right)\right)}

Simplify

The graph

Plot the graph f(x)

The answer [src]

   oo                   
    /                   
   |                    
   |         1          
4* |  --------------- dx
   |    /       2   \   
   |  x*\1 + log (x)/   
   |                    
  /                     
  1

4 \int\limits_{1}^{\infty} \frac{1}{x \left(\log{\left(x \right)}^{2} + 1\right)}\, dx

   oo                   
    /                   
   |                    
   |         1          
4* |  --------------- dx
   |    /       2   \   
   |  x*\1 + log (x)/   
   |                    
  /                     
  1

4 \int\limits_{1}^{\infty} \frac{1}{x \left(\log{\left(x \right)}^{2} + 1\right)}\, dx

4*Integral(1/(x*(1 + log(x)^2)), (x, 1, oo))

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of 4/(x(ln^2x+1)) dx

Limits of integration:

The graph:

Piecewise:

The solution