Sr Examen

Otras calculadoras

Resolución de integrales/ sh(ax)cos(bx)

Integral de sh(ax)cos(bx) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  0                      
  /                      
 |                       
 |  sinh(a*x)*cos(b*x) dx
 |                       
/                        
1
∫10cos⁡(bx)sinh⁡(ax) dx\int\limits_{1}^{0} \cos{\left(b x \right)} \sinh{\left(a x \right)}\, dx 
Integral(sinh(a*x)*cos(b*x), (x, 1, 0))
Respuesta (Indefinida) [src] 
                               //                     0                       for And(a = 0, b = 0)\
                               ||                                                                  |
                               ||                     2                                            |
                               ||               -I*sin (b*x)                                       |
                               ||               -------------                     for a = -I*b     |
                               ||                    2*b                                           |
  /                            ||                                                                  |
 |                             ||                     2                                            |
 | sinh(a*x)*cos(b*x) dx = C + |<                I*sin (b*x)                                       |
 |                             ||                -----------                       for a = I*b     |
/                              ||                    2*b                                           |
                               ||                                                                  |
                               ||a*cos(b*x)*cosh(a*x)   b*sin(b*x)*sinh(a*x)                       |
                               ||-------------------- + --------------------        otherwise      |
                               ||       2    2                 2    2                              |
                               ||      a  + b                 a  + b                               |
                               \\                                                                  /
∫cos⁡(bx)sinh⁡(ax) dx=C+{0for a=0∧b=0−isin⁡2(bx)2bfor a=−ibisin⁡2(bx)2bfor a=ibacos⁡(bx)cosh⁡(ax)a2+b2+bsin⁡(bx)sinh⁡(ax)a2+b2otherwise\int \cos{\left(b x \right)} \sinh{\left(a x \right)}\, dx = C + \begin{cases} 0 & \text{for}\: a = 0 \wedge b = 0 \\- \frac{i \sin^{2}{\left(b x \right)}}{2 b} & \text{for}\: a = - i b \\\frac{i \sin^{2}{\left(b x \right)}}{2 b} & \text{for}\: a = i b \\\frac{a \cos{\left(b x \right)} \cosh{\left(a x \right)}}{a^{2} + b^{2}} + \frac{b \sin{\left(b x \right)} \sinh{\left(a x \right)}}{a^{2} + b^{2}} & \text{otherwise} \end{cases}
Simplificar
Respuesta [src] 
/                      0                                     for Or(And(a = 0, b = 0), And(a = 0, a = -I*b, b = 0), And(a = 0, a = I*b, b = 0), And(a = 0, a = -I*b, a = I*b, b = 0))             
|                                                                                                                                                                                                 
|                          2                                                                                                                                                                      
|                I    I*cos (b)                                                                                                                                                                   
|               --- - ---------                 for Or(And(a = 0, a = -I*b), And(a = -I*b, a = I*b), And(a = -I*b, b = 0), And(a = 0, a = -I*b, a = I*b), And(a = -I*b, a = I*b, b = 0), a = -I*b)
|               2*b      2*b                                                                                                                                                                      
|                                                                                                                                                                                                 
|                           2                                                                                                                                                                     
<                 I    I*cos (b)                                                                                                                                                                  
|              - --- + ---------                                                            for Or(And(a = 0, a = I*b), And(a = I*b, b = 0), a = I*b)                                             
|                2*b      2*b                                                                                                                                                                     
|                                                                                                                                                                                                 
|   a      a*cos(b)*cosh(a)   b*sin(b)*sinh(a)                                                                                                                                                    
|------- - ---------------- - ----------------                                                                      otherwise                                                                     
| 2    2        2    2             2    2                                                                                                                                                         
|a  + b        a  + b             a  + b                                                                                                                                                          
\
{0for (a=0∧b=0)∨(a=0∧a=−ib∧b=0)∨(a=0∧a=ib∧b=0)∨(a=0∧a=−ib∧a=ib∧b=0)−icos⁡2(b)2b+i2bfor (a=0∧a=−ib)∨(a=−ib∧a=ib)∨(a=−ib∧b=0)∨(a=0∧a=−ib∧a=ib)∨(a=−ib∧a=ib∧b=0)∨a=−ibicos⁡2(b)2b−i2bfor (a=0∧a=ib)∨(a=ib∧b=0)∨a=ib−acos⁡(b)cosh⁡(a)a2+b2+aa2+b2−bsin⁡(b)sinh⁡(a)a2+b2otherwise\begin{cases} 0 & \text{for}\: \left(a = 0 \wedge b = 0\right) \vee \left(a = 0 \wedge a = - i b \wedge b = 0\right) \vee \left(a = 0 \wedge a = i b \wedge b = 0\right) \vee \left(a = 0 \wedge a = - i b \wedge a = i b \wedge b = 0\right) \\- \frac{i \cos^{2}{\left(b \right)}}{2 b} + \frac{i}{2 b} & \text{for}\: \left(a = 0 \wedge a = - i b\right) \vee \left(a = - i b \wedge a = i b\right) \vee \left(a = - i b \wedge b = 0\right) \vee \left(a = 0 \wedge a = - i b \wedge a = i b\right) \vee \left(a = - i b \wedge a = i b \wedge b = 0\right) \vee a = - i b \\\frac{i \cos^{2}{\left(b \right)}}{2 b} - \frac{i}{2 b} & \text{for}\: \left(a = 0 \wedge a = i b\right) \vee \left(a = i b \wedge b = 0\right) \vee a = i b \\- \frac{a \cos{\left(b \right)} \cosh{\left(a \right)}}{a^{2} + b^{2}} + \frac{a}{a^{2} + b^{2}} - \frac{b \sin{\left(b \right)} \sinh{\left(a \right)}}{a^{2} + b^{2}} & \text{otherwise} \end{cases} 
=
= 
/                      0                                     for Or(And(a = 0, b = 0), And(a = 0, a = -I*b, b = 0), And(a = 0, a = I*b, b = 0), And(a = 0, a = -I*b, a = I*b, b = 0))             
|                                                                                                                                                                                                 
|                          2                                                                                                                                                                      
|                I    I*cos (b)                                                                                                                                                                   
|               --- - ---------                 for Or(And(a = 0, a = -I*b), And(a = -I*b, a = I*b), And(a = -I*b, b = 0), And(a = 0, a = -I*b, a = I*b), And(a = -I*b, a = I*b, b = 0), a = -I*b)
|               2*b      2*b                                                                                                                                                                      
|                                                                                                                                                                                                 
|                           2                                                                                                                                                                     
<                 I    I*cos (b)                                                                                                                                                                  
|              - --- + ---------                                                            for Or(And(a = 0, a = I*b), And(a = I*b, b = 0), a = I*b)                                             
|                2*b      2*b                                                                                                                                                                     
|                                                                                                                                                                                                 
|   a      a*cos(b)*cosh(a)   b*sin(b)*sinh(a)                                                                                                                                                    
|------- - ---------------- - ----------------                                                                      otherwise                                                                     
| 2    2        2    2             2    2                                                                                                                                                         
|a  + b        a  + b             a  + b                                                                                                                                                          
\
{0for (a=0∧b=0)∨(a=0∧a=−ib∧b=0)∨(a=0∧a=ib∧b=0)∨(a=0∧a=−ib∧a=ib∧b=0)−icos⁡2(b)2b+i2bfor (a=0∧a=−ib)∨(a=−ib∧a=ib)∨(a=−ib∧b=0)∨(a=0∧a=−ib∧a=ib)∨(a=−ib∧a=ib∧b=0)∨a=−ibicos⁡2(b)2b−i2bfor (a=0∧a=ib)∨(a=ib∧b=0)∨a=ib−acos⁡(b)cosh⁡(a)a2+b2+aa2+b2−bsin⁡(b)sinh⁡(a)a2+b2otherwise\begin{cases} 0 & \text{for}\: \left(a = 0 \wedge b = 0\right) \vee \left(a = 0 \wedge a = - i b \wedge b = 0\right) \vee \left(a = 0 \wedge a = i b \wedge b = 0\right) \vee \left(a = 0 \wedge a = - i b \wedge a = i b \wedge b = 0\right) \\- \frac{i \cos^{2}{\left(b \right)}}{2 b} + \frac{i}{2 b} & \text{for}\: \left(a = 0 \wedge a = - i b\right) \vee \left(a = - i b \wedge a = i b\right) \vee \left(a = - i b \wedge b = 0\right) \vee \left(a = 0 \wedge a = - i b \wedge a = i b\right) \vee \left(a = - i b \wedge a = i b \wedge b = 0\right) \vee a = - i b \\\frac{i \cos^{2}{\left(b \right)}}{2 b} - \frac{i}{2 b} & \text{for}\: \left(a = 0 \wedge a = i b\right) \vee \left(a = i b \wedge b = 0\right) \vee a = i b \\- \frac{a \cos{\left(b \right)} \cosh{\left(a \right)}}{a^{2} + b^{2}} + \frac{a}{a^{2} + b^{2}} - \frac{b \sin{\left(b \right)} \sinh{\left(a \right)}}{a^{2} + b^{2}} & \text{otherwise} \end{cases} 
Piecewise((0, ((a = 0)∧(b = 0))∨((a = 0)∧(b = 0)∧(a = i*b))∨((a = 0)∧(b = 0)∧(a = -i*b))∨((a = 0)∧(b = 0)∧(a = i*b)∧(a = -i*b))), (i/(2*b) - i*cos(b)^2/(2*b), (a = -i*b)∨((a = 0)∧(a = -i*b))∨((b = 0)∧(a = -i*b))∨((a = i*b)∧(a = -i*b))∨((a = 0)∧(a = i*b)∧(a = -i*b))∨((b = 0)∧(a = i*b)∧(a = -i*b))), (-i/(2*b) + i*cos(b)^2/(2*b), (a = i*b)∨((a = 0)∧(a = i*b))∨((b = 0)∧(a = i*b))), (a/(a^2 + b^2) - a*cos(b)*cosh(a)/(a^2 + b^2) - b*sin(b)*sinh(a)/(a^2 + b^2), True))

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

    © Sr Examen – Калькулятор