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Solving integrals/ tan²x/1+x²

Integral of tan²x/1+x² dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                  
  /                  
 |                   
 |  /   2        \   
 |  |tan (x)    2|   
 |  |------- + x | dx
 |  \   1        /   
 |                   
/                    
0
$$\int\limits_{0}^{1} \left(x^{2} + \frac{\tan^{2}{\left(x \right)}}{1}\right)\, dx$$ 
Integral(tan(x)^2/1 + x^2, (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

    1. The integral of is when :

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

      1. Don't know the steps in finding this integral.

        But the integral is

      So, the result is:

    The result is:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                       
 |                                        
 | /   2        \               3         
 | |tan (x)    2|              x    sin(x)
 | |------- + x | dx = C - x + -- + ------
 | \   1        /              3    cos(x)
 |                                        
/
$$\int \left(x^{2} + \frac{\tan^{2}{\left(x \right)}}{1}\right)\, dx = C + \frac{x^{3}}{3} - x + \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  2   sin(1)
- - + ------
  3   cos(1)
$$- \frac{2}{3} + \frac{\sin{\left(1 \right)}}{\cos{\left(1 \right)}}$$ 
=
= 
  2   sin(1)
- - + ------
  3   cos(1)
$$- \frac{2}{3} + \frac{\sin{\left(1 \right)}}{\cos{\left(1 \right)}}$$ 
-2/3 + sin(1)/cos(1)
Numerical answer [src] 
0.890741057988236
0.890741057988236

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

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