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Resolución de integrales/ exp(a*x)/ exp(a*x)*sin(b*x+c)

Integral de exp(a*x)*sin(b*x+c) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                     
  /                     
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 |   a*x                
 |  e   *sin(b*x + c) dx
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/                       
0
∫01eaxsin⁡(bx+c) dx\int\limits_{0}^{1} e^{a x} \sin{\left(b x + c \right)}\, dx 
Integral(exp(a*x)*sin(b*x + c), (x, 0, 1))
Respuesta (Indefinida) [src] 
                                                                  //                                                                                                                                                /                                   /c   b*x\                                                                                                                                                                        \
                                                                  ||                                                                                                                                                |                          2*b*x*tan|- + ---|                                                                                                                                                                        |
                                                                  ||                                                                                                                                                |          2                        \2    2 /                                                                                                                                                                        |
                                                                  ||                                                                                                                                                |--------------------- + ---------------------  for b != 0                                                                                                                                                           |
                                                                  ||                                                                                                                                                | 2    2    2/c   b*x\    2    2    2/c   b*x\                                                                                                                                                                       |
                                                                  ||                                                                                                                                                |b  + b *tan |- + ---|   b  + b *tan |- + ---|                                                                                                                                                                       |
                                                                  ||                                                                                                                                                <            \2    2 /               \2    2 /                                                                                                                                                              for a = 0|
                                                                  ||                                                                                                                                                |                                                                                                                                                                                                                    |
                                                                  ||                                                                                                                                                |                   2                                                                                                                                                                                                |
                                                                  ||                                                                                                                                                |                  x *cos(c)                                                                                                                                                                                         |
                                                                  ||                                                                                                                                                |                  ---------                    otherwise                                                                                                                                                            |
                                                                  ||                                                                                                                                                |                      2                                                                                                                                                                                             |
                                                                  ||                                                                                                                                                \                                                                                                                                                                                                                    |
                                                                  ||                                                                                                                                                                                                                                                                                                                                                                     |
                                                                  ||  //                                                                                                           /         /c   b*x\                                       2/c   b*x\                                                                                                                                    \                                             |
                                                                  ||  ||                                                                                                           |    2*tan|- + ---|                                b*x*tan |- + ---|                                                                                                                                    |                                             |
                                                                  ||  ||                                                                                                           |         \2    2 /               b*x                      \2    2 /                                                                                                                                    |                                             |
                                                                  ||  ||                                                                                                           |--------------------- - --------------------- + ---------------------  for b != 0                                                                                                                      |                                             |
                                                                  ||  ||                                                                                                           | 2    2    2/c   b*x\    2    2    2/c   b*x\    2    2    2/c   b*x\                                                                                                                                  |                                             |
                                                                  ||  ||                                                                                                           |b  + b *tan |- + ---|   b  + b *tan |- + ---|   b  + b *tan |- + ---|                                                                                                                                  |                                             |
                                                                  ||  ||                                                                                                           <            \2    2 /               \2    2 /               \2    2 /                                                                                                                         for a = 0|                                             |
                                                                  ||  ||                                                                                                           |                                                                                                                                                                                                       |                                             |
                                                                  ||  ||                                                                                                           |                               2                                                                                                                                                                       |                                             |
                                                                  ||  ||                                                                                                           |                              x *sin(c)                                                                                                                                                                |                                             |
                                                                  ||  ||                                                                                                           |                              ---------                                otherwise                                                                                                                       |                                             |
                                                                  ||  ||                                                                                                           |                                  2                                                                                                                                                                    |                                             |
                                                                  ||  ||                                                                                                           \                                                                                                                                                                                                       |                                             |
                                                                  ||  ||                                                                                                                                                                                                                                                                                                                   |                                             |
                                                                  ||  ||                                    //                                                                                              /                                   /c   b*x\                                                                                                                      \           |                                             |
                                                                  ||  ||                                    ||                                                                                              |                          2*b*x*tan|- + ---|                                                                                                                      |           |                                             |
                                                                  ||  ||                                    ||                                                                                              |          2                        \2    2 /                                                                                                                      |           |                                             |
                                                                  ||  ||                                    ||                                                                                              |--------------------- + ---------------------  for b != 0                                                                                                         |           |                                             |
                                                                  ||  ||                                    ||                                                                                              | 2    2    2/c   b*x\    2    2    2/c   b*x\                                                                                                                     |           |                                             |
                                                                  ||  ||                                    ||                                                                                              |b  + b *tan |- + ---|   b  + b *tan |- + ---|                                                                                                                     |           |                                             |
                                                                  ||  ||                                    ||                                                                                              <            \2    2 /               \2    2 /                                                                                                            for a = 0|           |                                             |
                                                                  ||  ||                                    ||                                                                                              |                                                                                                                                                                  |           |                                             |
                                                                  ||  ||                                    ||                                                                                              |                   2                                                                                                                                              |           |                                             |
                                                                  ||  ||                                    ||                                                                                              |                  x *cos(c)                                                                                                                                       |           |                                             |
                                                                  ||  ||                                    ||                                                                                              |                  ---------                    otherwise                                                                                                          |           |                                             |
                                                                  ||  ||                                    ||                                                                                              |                      2                                                                                                                                           |           |                                             |
                                                                  ||  ||                                    ||                                                                                              \                                                                                                                                                                  |           |                                             |
                                                                  ||  ||                                    ||                                                                                                                                                                                                                                                                 |           |                                             |
                                                                  ||  ||                                    ||  //                                                         /         /c   b*x\                                       2/c   b*x\                                                                                  \                                             |           |                                             |
                                                                  ||  ||                                    ||  ||                                                         |    2*tan|- + ---|                                b*x*tan |- + ---|                                                                                  |                                             |           |                                             |
                                                                  ||  ||                                    ||  ||                                                         |         \2    2 /               b*x                      \2    2 /                                                                                  |                                             |           |                                             |
                                                                  ||  ||                                    ||  ||                                                         |--------------------- - --------------------- + ---------------------  for b != 0                                                                    |                                             |           |                                             |
                                                                  ||  ||                                    ||  ||                                                         | 2    2    2/c   b*x\    2    2    2/c   b*x\    2    2    2/c   b*x\                                                                                |                                             |           |                                             |
                                                                  ||  ||                                    ||  ||                                                         |b  + b *tan |- + ---|   b  + b *tan |- + ---|   b  + b *tan |- + ---|                                                                                |                                             |           |                                             |
                                                                  ||  ||                                    ||  ||                                                         <            \2    2 /               \2    2 /               \2    2 /                                                                       for a = 0|                                             |           |                                             |
                                                                  ||  ||                                    ||  ||                                                         |                                                                                                                                                     |                                             |           |                                             |
                                                                  ||  ||                                    ||  ||                                                         |                               2                                                                                                                     |                                             |           |                                             |
                                                                  ||  ||                                    ||  ||                                                         |                              x *sin(c)                                                                                                              |                                             |           |                                             |
                                                                  ||  ||                                    ||  ||                                                         |                              ---------                                otherwise                                                                     |                                             |           |                                             |
  /                           // x    for a = 0\                  ||  ||                                    ||  ||                                                         |                                  2                                                                                                                  |                                             |           |                                             |
 |                            ||               |                  ||  ||                                    ||  ||                                                         \                                                                                                                                                     |                                             |           |                                             |
 |  a*x                       || a*x           |                  ||  ||                                    ||  ||                                                                                                                                                                                                               |                                             |           |                                             |
 | e   *sin(b*x + c) dx = C + |
∫eaxsin⁡(bx+c) dx=C−b({{2bxtan⁡(bx2+c2)b2tan⁡2(bx2+c2)+b2+2b2tan⁡2(bx2+c2)+b2for b≠0x2cos⁡(c)2otherwisefor a=0b({{bxtan⁡2(bx2+c2)b2tan⁡2(bx2+c2)+b2−bxb2tan⁡2(bx2+c2)+b2+2tan⁡(bx2+c2)b2tan⁡2(bx2+c2)+b2for b≠0x2sin⁡(c)2otherwisefor a=0−b({{2bxtan⁡(bx2+c2)b2tan⁡2(bx2+c2)+b2+2b2tan⁡2(bx2+c2)+b2for b≠0x2cos⁡(c)2otherwisefor a=0b({{bxtan⁡2(bx2+c2)b2tan⁡2(bx2+c2)+b2−bxb2tan⁡2(bx2+c2)+b2+2tan⁡(bx2+c2)b2tan⁡2(bx2+c2)+b2for b≠0x2sin⁡(c)2otherwisefor a=0−b({{2bxtan⁡(bx2+c2)b2tan⁡2(bx2+c2)+b2+2b2tan⁡2(bx2+c2)+b2for b≠0x2cos⁡(c)2otherwisefor a=0b({{bxtan⁡2(bx2+c2)b2tan⁡2(bx2+c2)+b2−bxb2tan⁡2(bx2+c2)+b2+2tan⁡(bx2+c2)b2tan⁡2(bx2+c2)+b2for b≠0x2sin⁡(c)2otherwisefor a=0{xsin⁡(c)for a=0∧b=0xe−ibxsin⁡(bx+c)2−ixe−ibxcos⁡(bx+c)2−e−ibxcos⁡(bx+c)2bfor a=−ibxeibxsin⁡(bx+c)2+ixeibxcos⁡(bx+c)2−eibxcos⁡(bx+c)2bfor a=ibaeaxsin⁡(bx+c)a2+b2−beaxcos⁡(bx+c)a2+b2otherwiseaotherwise)+({xfor a=0eaxaotherwise)cos⁡(bx+c)aotherwise)+({xfor a=0eaxaotherwise)sin⁡(bx+c)aotherwise)+({xfor a=0eaxaotherwise)cos⁡(bx+c)aotherwise)+({xfor a=0eaxaotherwise)sin⁡(bx+c)aotherwise)+({xfor a=0eaxaotherwise)cos⁡(bx+c)aotherwise)+({xfor a=0eaxaotherwise)sin⁡(bx+c)\int e^{a x} \sin{\left(b x + c \right)}\, dx = C - b \left(\begin{cases} \begin{cases} \frac{2 b x \tan{\left(\frac{b x}{2} + \frac{c}{2} \right)}}{b^{2} \tan^{2}{\left(\frac{b x}{2} + \frac{c}{2} \right)} + b^{2}} + \frac{2}{b^{2} \tan^{2}{\left(\frac{b x}{2} + \frac{c}{2} \right)} + b^{2}} & \text{for}\: b \neq 0 \\\frac{x^{2} \cos{\left(c \right)}}{2} & \text{otherwise} \end{cases} & \text{for}\: a = 0 \\\frac{b \left(\begin{cases} \begin{cases} \frac{b x \tan^{2}{\left(\frac{b x}{2} + \frac{c}{2} \right)}}{b^{2} \tan^{2}{\left(\frac{b x}{2} + \frac{c}{2} \right)} + b^{2}} - \frac{b x}{b^{2} \tan^{2}{\left(\frac{b x}{2} + \frac{c}{2} \right)} + b^{2}} + \frac{2 \tan{\left(\frac{b x}{2} + \frac{c}{2} \right)}}{b^{2} \tan^{2}{\left(\frac{b x}{2} + \frac{c}{2} \right)} + b^{2}} & \text{for}\: b \neq 0 \\\frac{x^{2} \sin{\left(c \right)}}{2} & \text{otherwise} \end{cases} & \text{for}\: a = 0 \\\frac{- b \left(\begin{cases} \begin{cases} \frac{2 b x \tan{\left(\frac{b x}{2} + \frac{c}{2} \right)}}{b^{2} \tan^{2}{\left(\frac{b x}{2} + \frac{c}{2} \right)} + b^{2}} + \frac{2}{b^{2} \tan^{2}{\left(\frac{b x}{2} + \frac{c}{2} \right)} + b^{2}} & \text{for}\: b \neq 0 \\\frac{x^{2} \cos{\left(c \right)}}{2} & \text{otherwise} \end{cases} & \text{for}\: a = 0 \\\frac{b \left(\begin{cases} \begin{cases} \frac{b x \tan^{2}{\left(\frac{b x}{2} + \frac{c}{2} \right)}}{b^{2} \tan^{2}{\left(\frac{b x}{2} + \frac{c}{2} \right)} + b^{2}} - \frac{b x}{b^{2} \tan^{2}{\left(\frac{b x}{2} + \frac{c}{2} \right)} + b^{2}} + \frac{2 \tan{\left(\frac{b x}{2} + \frac{c}{2} \right)}}{b^{2} \tan^{2}{\left(\frac{b x}{2} + \frac{c}{2} \right)} + b^{2}} & \text{for}\: b \neq 0 \\\frac{x^{2} \sin{\left(c \right)}}{2} & \text{otherwise} \end{cases} & \text{for}\: a = 0 \\\frac{- b \left(\begin{cases} \begin{cases} \frac{2 b x \tan{\left(\frac{b x}{2} + \frac{c}{2} \right)}}{b^{2} \tan^{2}{\left(\frac{b x}{2} + \frac{c}{2} \right)} + b^{2}} + \frac{2}{b^{2} \tan^{2}{\left(\frac{b x}{2} + \frac{c}{2} \right)} + b^{2}} & \text{for}\: b \neq 0 \\\frac{x^{2} \cos{\left(c \right)}}{2} & \text{otherwise} \end{cases} & \text{for}\: a = 0 \\\frac{b \left(\begin{cases} \begin{cases} \frac{b x \tan^{2}{\left(\frac{b x}{2} + \frac{c}{2} \right)}}{b^{2} \tan^{2}{\left(\frac{b x}{2} + \frac{c}{2} \right)} + b^{2}} - \frac{b x}{b^{2} \tan^{2}{\left(\frac{b x}{2} + \frac{c}{2} \right)} + b^{2}} + \frac{2 \tan{\left(\frac{b x}{2} + \frac{c}{2} \right)}}{b^{2} \tan^{2}{\left(\frac{b x}{2} + \frac{c}{2} \right)} + b^{2}} & \text{for}\: b \neq 0 \\\frac{x^{2} \sin{\left(c \right)}}{2} & \text{otherwise} \end{cases} & \text{for}\: a = 0 \\\frac{\begin{cases} x \sin{\left(c \right)} & \text{for}\: a = 0 \wedge b = 0 \\\frac{x e^{- i b x} \sin{\left(b x + c \right)}}{2} - \frac{i x e^{- i b x} \cos{\left(b x + c \right)}}{2} - \frac{e^{- i b x} \cos{\left(b x + c \right)}}{2 b} & \text{for}\: a = - i b \\\frac{x e^{i b x} \sin{\left(b x + c \right)}}{2} + \frac{i x e^{i b x} \cos{\left(b x + c \right)}}{2} - \frac{e^{i b x} \cos{\left(b x + c \right)}}{2 b} & \text{for}\: a = i b \\\frac{a e^{a x} \sin{\left(b x + c \right)}}{a^{2} + b^{2}} - \frac{b e^{a x} \cos{\left(b x + c \right)}}{a^{2} + b^{2}} & \text{otherwise} \end{cases}}{a} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} x & \text{for}\: a = 0 \\\frac{e^{a x}}{a} & \text{otherwise} \end{cases}\right) \cos{\left(b x + c \right)}}{a} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} x & \text{for}\: a = 0 \\\frac{e^{a x}}{a} & \text{otherwise} \end{cases}\right) \sin{\left(b x + c \right)}}{a} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} x & \text{for}\: a = 0 \\\frac{e^{a x}}{a} & \text{otherwise} \end{cases}\right) \cos{\left(b x + c \right)}}{a} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} x & \text{for}\: a = 0 \\\frac{e^{a x}}{a} & \text{otherwise} \end{cases}\right) \sin{\left(b x + c \right)}}{a} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} x & \text{for}\: a = 0 \\\frac{e^{a x}}{a} & \text{otherwise} \end{cases}\right) \cos{\left(b x + c \right)}}{a} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} x & \text{for}\: a = 0 \\\frac{e^{a x}}{a} & \text{otherwise} \end{cases}\right) \sin{\left(b x + c \right)}
Simplificar
Respuesta [src] 
/                             sin(c)                                             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))             
|                                                                                                                                                                                                                     
|          -I*b                            -I*b               -I*b                                                                                                                                                    
|cos(c)   e    *sin(b + c)   I*cos(b + c)*e       cos(b + c)*e                                                                                                                                                        
|------ + ---------------- - ------------------ - ----------------  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                   2                  2*b                                                                                                                                                           
|                                                                                                                                                                                                                     
|           I*b                            I*b               I*b                                                                                                                                                      
< cos(c)   e   *sin(b + c)   I*cos(b + c)*e      cos(b + c)*e                                                                                                                                                         
| ------ + --------------- + ----------------- - ---------------                                                for Or(And(a = 0, a = I*b), And(a = I*b, b = 0), a = I*b)                                             
|  2*b            2                  2                 2*b                                                                                                                                                            
|                                                                                                                                                                                                                     
|                              a                            a                                                                                                                                                         
|     b*cos(c)   a*sin(c)   a*e *sin(b + c)   b*cos(b + c)*e                                                                                                                                                          
|     -------- - -------- + --------------- - ---------------                                                                           otherwise                                                                     
|      2    2     2    2         2    2            2    2                                                                                                                                                             
\     a  + b     a  + b         a  + b            a  + b
{sin⁡(c)for (a=0∧b=0)∨(a=0∧a=−ib∧b=0)∨(a=0∧a=ib∧b=0)∨(a=0∧a=−ib∧a=ib∧b=0)e−ibsin⁡(b+c)2−ie−ibcos⁡(b+c)2+cos⁡(c)2b−e−ibcos⁡(b+c)2bfor (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=−ibeibsin⁡(b+c)2+ieibcos⁡(b+c)2−eibcos⁡(b+c)2b+cos⁡(c)2bfor (a=0∧a=ib)∨(a=ib∧b=0)∨a=ibaeasin⁡(b+c)a2+b2−asin⁡(c)a2+b2−beacos⁡(b+c)a2+b2+bcos⁡(c)a2+b2otherwise\begin{cases} \sin{\left(c \right)} & \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{e^{- i b} \sin{\left(b + c \right)}}{2} - \frac{i e^{- i b} \cos{\left(b + c \right)}}{2} + \frac{\cos{\left(c \right)}}{2 b} - \frac{e^{- i b} \cos{\left(b + c \right)}}{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{e^{i b} \sin{\left(b + c \right)}}{2} + \frac{i e^{i b} \cos{\left(b + c \right)}}{2} - \frac{e^{i b} \cos{\left(b + c \right)}}{2 b} + \frac{\cos{\left(c \right)}}{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 e^{a} \sin{\left(b + c \right)}}{a^{2} + b^{2}} - \frac{a \sin{\left(c \right)}}{a^{2} + b^{2}} - \frac{b e^{a} \cos{\left(b + c \right)}}{a^{2} + b^{2}} + \frac{b \cos{\left(c \right)}}{a^{2} + b^{2}} & \text{otherwise} \end{cases} 
=
= 
/                             sin(c)                                             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))             
|                                                                                                                                                                                                                     
|          -I*b                            -I*b               -I*b                                                                                                                                                    
|cos(c)   e    *sin(b + c)   I*cos(b + c)*e       cos(b + c)*e                                                                                                                                                        
|------ + ---------------- - ------------------ - ----------------  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                   2                  2*b                                                                                                                                                           
|                                                                                                                                                                                                                     
|           I*b                            I*b               I*b                                                                                                                                                      
< cos(c)   e   *sin(b + c)   I*cos(b + c)*e      cos(b + c)*e                                                                                                                                                         
| ------ + --------------- + ----------------- - ---------------                                                for Or(And(a = 0, a = I*b), And(a = I*b, b = 0), a = I*b)                                             
|  2*b            2                  2                 2*b                                                                                                                                                            
|                                                                                                                                                                                                                     
|                              a                            a                                                                                                                                                         
|     b*cos(c)   a*sin(c)   a*e *sin(b + c)   b*cos(b + c)*e                                                                                                                                                          
|     -------- - -------- + --------------- - ---------------                                                                           otherwise                                                                     
|      2    2     2    2         2    2            2    2                                                                                                                                                             
\     a  + b     a  + b         a  + b            a  + b
{sin⁡(c)for (a=0∧b=0)∨(a=0∧a=−ib∧b=0)∨(a=0∧a=ib∧b=0)∨(a=0∧a=−ib∧a=ib∧b=0)e−ibsin⁡(b+c)2−ie−ibcos⁡(b+c)2+cos⁡(c)2b−e−ibcos⁡(b+c)2bfor (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=−ibeibsin⁡(b+c)2+ieibcos⁡(b+c)2−eibcos⁡(b+c)2b+cos⁡(c)2bfor (a=0∧a=ib)∨(a=ib∧b=0)∨a=ibaeasin⁡(b+c)a2+b2−asin⁡(c)a2+b2−beacos⁡(b+c)a2+b2+bcos⁡(c)a2+b2otherwise\begin{cases} \sin{\left(c \right)} & \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{e^{- i b} \sin{\left(b + c \right)}}{2} - \frac{i e^{- i b} \cos{\left(b + c \right)}}{2} + \frac{\cos{\left(c \right)}}{2 b} - \frac{e^{- i b} \cos{\left(b + c \right)}}{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{e^{i b} \sin{\left(b + c \right)}}{2} + \frac{i e^{i b} \cos{\left(b + c \right)}}{2} - \frac{e^{i b} \cos{\left(b + c \right)}}{2 b} + \frac{\cos{\left(c \right)}}{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 e^{a} \sin{\left(b + c \right)}}{a^{2} + b^{2}} - \frac{a \sin{\left(c \right)}}{a^{2} + b^{2}} - \frac{b e^{a} \cos{\left(b + c \right)}}{a^{2} + b^{2}} + \frac{b \cos{\left(c \right)}}{a^{2} + b^{2}} & \text{otherwise} \end{cases} 
Piecewise((sin(c), ((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))), (cos(c)/(2*b) + exp(-i*b)*sin(b + c)/2 - i*cos(b + c)*exp(-i*b)/2 - cos(b + c)*exp(-i*b)/(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))), (cos(c)/(2*b) + exp(i*b)*sin(b + c)/2 + i*cos(b + c)*exp(i*b)/2 - cos(b + c)*exp(i*b)/(2*b), (a = i*b)∨((a = 0)∧(a = i*b))∨((b = 0)∧(a = i*b))), (b*cos(c)/(a^2 + b^2) - a*sin(c)/(a^2 + b^2) + a*exp(a)*sin(b + c)/(a^2 + b^2) - b*cos(b + c)*exp(a)/(a^2 + b^2), True))

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

    © Sr Examen – Калькулятор