Mister Exam

Other calculators

Solving integrals/ ln^2x/1+x^2

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                  
  /                  
 |                   
 |  /   2        \   
 |  |log (x)    2|   
 |  |------- + x | dx
 |  \   1        /   
 |                   
/                    
0
∫01(x2+log⁡(x)21) dx\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

  1. Integrate term-by-term:

    1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

      ∫x2 dx=x33\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:

      ∫log⁡(x)21 dx=∫log⁡(x)2 dx\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

        xlog⁡(x)2−2xlog⁡(x)+2xx \log{\left(x \right)}^{2} - 2 x \log{\left(x \right)} + 2 x

      So, the result is: xlog⁡(x)2−2xlog⁡(x)+2xx \log{\left(x \right)}^{2} - 2 x \log{\left(x \right)} + 2 x

    The result is: x33+xlog⁡(x)2−2xlog⁡(x)+2x\frac{x^{3}}{3} + x \log{\left(x \right)}^{2} - 2 x \log{\left(x \right)} + 2 x

  2. Now simplify:

    x(x2+3log⁡(x)2−6log⁡(x)+6)3\frac{x \left(x^{2} + 3 \log{\left(x \right)}^{2} - 6 \log{\left(x \right)} + 6\right)}{3}

  3. Add the constant of integration:

    x(x2+3log⁡(x)2−6log⁡(x)+6)3+constant\frac{x \left(x^{2} + 3 \log{\left(x \right)}^{2} - 6 \log{\left(x \right)} + 6\right)}{3}+ \mathrm{constant}

The answer is:

x(x2+3log⁡(x)2−6log⁡(x)+6)3+constant\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 ((log⁡x)2−2 log⁡x+2)+x33x\,\left(\left(\log x\right)^2-2\,\log x+2\right)+{{x^3}\over{3}}
Simplify
The answer [src] 
7/3
73{{7}\over{3}} 
=
= 
7/3
73\frac{7}{3}
Simplify
Numerical answer [src] 
2.33333333333333
2.33333333333333

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

    © Mister Exam – Calculator