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Identical expressions
two (tgx)^ two + one
2(tgx) squared plus 1
two (tgx) to the power of two plus one
2(tgx)2+1
2tgx2+1
2(tgx)²+1
2(tgx) to the power of 2+1
2tgx^2+1
2(tgx)^2+1dx
Similar expressions
2(tgx)^2-1

Solving integrals/ 2(tgx)^2+1

Integral of 2(tgx)^2+1 dx

The solution

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  1                   
  /                   
 |                    
 |  /     2       \   
 |  \2*tan (x) + 1/ dx
 |                    
/                     
0

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

Integral(2*tan(x)^2 + 1, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 2 \tan^{2}{\left(x \right)}\, dx = 2 \int \tan^{2}{\left(x \right)}\, dx$
  1. Rewrite the integrand:
    
    $\tan^{2}{\left(x \right)} = \sec^{2}{\left(x \right)} - 1$
  2. Integrate term-by-term:
    1. $\int \sec^{2}{\left(x \right)}\, dx = \tan{\left(x \right)}$
    1. The integral of a constant is the constant times the variable of integration:
      
      $\int \left(-1\right)\, dx = - x$
    The result is: $- x + \tan{\left(x \right)}$
  So, the result is: $- 2 x + 2 \tan{\left(x \right)}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 1\, dx = x$
The result is: $- x + 2 \tan{\left(x \right)}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

$$2\,\left(\tan x-x\right)+x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

     2*sin(1)
-1 + --------
      cos(1)

$$2\,\tan 1-1$$

     2*sin(1)
-1 + --------
      cos(1)

$$-1 + \frac{2 \sin{\left(1 \right)}}{\cos{\left(1 \right)}}$$

Simplify

Numerical answer [src]

2.1148154493098

2.1148154493098

The graph

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

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Integral of 2(tgx)^2+1 dx

Limits of integration:

The graph:

Piecewise:

The solution