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Resolución de integrales/ cos^2/ tgx-1/ (e^(2*tgx-1)/cos^2(x))

Integral de (e^(2*tgx-1)/cos^2(x)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                 
  /                 
 |                  
 |   2*tan(x) - 1   
 |  E               
 |  ------------- dx
 |        2         
 |     cos (x)      
 |                  
/                   
0
$$\int\limits_{0}^{1} \frac{e^{2 \tan{\left(x \right)} - 1}}{\cos^{2}{\left(x \right)}}\, dx$$ 
Integral(E^(2*tan(x) - 1)/cos(x)^2, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                       /  /            \    
 |                        | |             |    
 |  2*tan(x) - 1          | |  2*tan(x)   |    
 | E                      | | e           |  -1
 | ------------- dx = C + | | --------- dx|*e  
 |       2                | |     2       |    
 |    cos (x)             | |  cos (x)    |    
 |                        | |             |    
/                         \/              /
$$\int \frac{e^{2 \tan{\left(x \right)} - 1}}{\cos^{2}{\left(x \right)}}\, dx = C + \frac{\int \frac{e^{2 \tan{\left(x \right)}}}{\cos^{2}{\left(x \right)}}\, dx}{e}$$
Simplificar
Respuesta [src] 
/  1             \    
|  /             |    
| |              |    
| |   2*tan(x)   |    
| |  e           |  -1
| |  --------- dx|*e  
| |      2       |    
| |   cos (x)    |    
| |              |    
|/               |    
\0               /
$$\frac{\int\limits_{0}^{1} \frac{e^{2 \tan{\left(x \right)}}}{\cos^{2}{\left(x \right)}}\, dx}{e}$$ 
=
= 
/  1             \    
|  /             |    
| |              |    
| |   2*tan(x)   |    
| |  e           |  -1
| |  --------- dx|*e  
| |      2       |    
| |   cos (x)    |    
| |              |    
|/               |    
\0               /
$$\frac{\int\limits_{0}^{1} \frac{e^{2 \tan{\left(x \right)}}}{\cos^{2}{\left(x \right)}}\, dx}{e}$$ 
Integral(exp(2*tan(x))/cos(x)^2, (x, 0, 1))*exp(-1)
Respuesta numérica [src] 
3.96008830866593
3.96008830866593

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

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