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Similar expressions
ln^2x/1-x^2

Integral of ln^2x/1+x^2 dx

The solution

You have entered [src]

  1                  
  /                  
 |                   
 |  /   2        \   
 |  |log (x)    2|   
 |  |------- + x | dx
 |  \   1        /   
 |                   
/                    
0

$$\int\limits_{0}^{1} \left(x^{2} + \frac{\log{\left(x \right)}^{2}}{1}\right)\, dx$$

Integral(log(x)^2/1 + x^2, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{2}\, dx = \frac{x^{3}}{3}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{\log{\left(x \right)}^{2}}{1}\, dx = \int \log{\left(x \right)}^{2}\, dx$
  1. Don't know the steps in finding this integral.
    
    But the integral is
    
    $x \log{\left(x \right)}^{2} - 2 x \log{\left(x \right)} + 2 x$
  So, the result is: $x \log{\left(x \right)}^{2} - 2 x \log{\left(x \right)} + 2 x$
The result is: $\frac{x^{3}}{3} + x \log{\left(x \right)}^{2} - 2 x \log{\left(x \right)} + 2 x$
Now simplify:

$\frac{x \left(x^{2} + 3 \log{\left(x \right)}^{2} - 6 \log{\left(x \right)} + 6\right)}{3}$
Add the constant of integration:

$\frac{x \left(x^{2} + 3 \log{\left(x \right)}^{2} - 6 \log{\left(x \right)} + 6\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x^{2} + 3 \log{\left(x \right)}^{2} - 6 \log{\left(x \right)} + 6\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                         
 |                                                          
 | /   2        \                 3                         
 | |log (x)    2|                x         2                
 | |------- + x | dx = C + 2*x + -- + x*log (x) - 2*x*log(x)
 | \   1        /                3                          
 |                                                          
/

$$x\,\left(\left(\log x\right)^2-2\,\log x+2\right)+{{x^3}\over{3}}$$

Simplify

The answer [src]

7/3

$${{7}\over{3}}$$

7/3

$$\frac{7}{3}$$

Simplify

Numerical answer [src]

2.33333333333333

2.33333333333333

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

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Integral of ln^2x/1+x^2 dx

Limits of integration:

The graph:

Piecewise:

The solution