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tan²x/ one +x²
tangent of ²x divide by 1 plus x²
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tan²x/1+x²dx
Similar expressions
tan²x/1-x²

Integral of tan²x/1+x² dx

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

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:
  
  $\int \frac{\tan^{2}{\left(x \right)}}{1}\, dx = \int \tan^{2}{\left(x \right)}\, dx$
  1. Don't know the steps in finding this integral.
    
    But the integral is
    
    $- x + \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}$
  So, the result is: $- x + \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}$
The result is: $\frac{x^{3}}{3} - x + \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}$
Now simplify:

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

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

The answer is:

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

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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Integral of tan²x/1+x² dx

Limits of integration:

The graph:

Piecewise:

The solution