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Resolución de integrales/ sec^3/ tan^3/ 15a(tan^3at*sec^3at)*dt

Integral de 15a(tan^3at*sec^3at)*dt dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                            
  /                            
 |                             
 |          3         3        
 |  15*a*tan (a*t)*sec (a*t) dt
 |                             
/                              
0
∫0115atan⁡3(at)sec⁡3(at) dt\int\limits_{0}^{1} 15 a \tan^{3}{\left(a t \right)} \sec^{3}{\left(a t \right)}\, dt 
Integral((15*a)*(tan(a*t)^3*sec(a*t)^3), (t, 0, 1))
Respuesta (Indefinida) [src] 
                                          //           0             for a = 0\
  /                                       ||                                  |
 |                                        ||     3           5                |
 |         3         3                    ||  sec (a*t)   sec (a*t)           |
 | 15*a*tan (a*t)*sec (a*t) dt = C + 15*a*|<- --------- + ---------           |
 |                                        ||      3           5               |
/                                         ||-----------------------  otherwise|
                                          ||           a                      |
                                          \\                                  /
∫15atan⁡3(at)sec⁡3(at) dt=C+15a({0for a=0sec⁡5(at)5−sec⁡3(at)3aotherwise)\int 15 a \tan^{3}{\left(a t \right)} \sec^{3}{\left(a t \right)}\, dt = C + 15 a \left(\begin{cases} 0 & \text{for}\: a = 0 \\\frac{\frac{\sec^{5}{\left(a t \right)}}{5} - \frac{\sec^{3}{\left(a t \right)}}{3}}{a} & \text{otherwise} \end{cases}\right)
Simplificar
Respuesta [src] 
/              2                                     
|    -3 + 5*cos (a)                                  
|2 - --------------  for And(a > -oo, a < oo, a != 0)
<          5                                         
|       cos (a)                                      
|                                                    
\        0                      otherwise
{−5cos⁡2(a)−3cos⁡5(a)+2for a>−∞∧a<∞∧a≠00otherwise\begin{cases} - \frac{5 \cos^{2}{\left(a \right)} - 3}{\cos^{5}{\left(a \right)}} + 2 & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\0 & \text{otherwise} \end{cases} 
=
= 
/              2                                     
|    -3 + 5*cos (a)                                  
|2 - --------------  for And(a > -oo, a < oo, a != 0)
<          5                                         
|       cos (a)                                      
|                                                    
\        0                      otherwise
{−5cos⁡2(a)−3cos⁡5(a)+2for a>−∞∧a<∞∧a≠00otherwise\begin{cases} - \frac{5 \cos^{2}{\left(a \right)} - 3}{\cos^{5}{\left(a \right)}} + 2 & \text{for}\: a > -\infty \wedge a < \infty \wedge a \neq 0 \\0 & \text{otherwise} \end{cases} 
Piecewise((2 - (-3 + 5*cos(a)^2)/cos(a)^5, (a > -oo)∧(a < oo)∧(Ne(a, 0))), (0, True))

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

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