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Resolución de integrales/ e^x*dx/ sqrt(2)/ e^x*dx/(sqrt(2)-e)^x

Integral de e^x*dx/(sqrt(2)-e)^x dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
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0
∫01ex(−e+2)x dx\int\limits_{0}^{1} \frac{e^{x}}{\left(- e + \sqrt{2}\right)^{x}}\, dx 
Integral(E^x/(sqrt(2) - E)^x, (x, 0, 1))
Respuesta (Indefinida) [src] 
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 |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        
 |       x                                                                                                                                                                                                      2/      ___\  x                                                                                                                                                                                                                                                                                                                                                                                  2  x                                                                                                                                                                                                                                                                                                                                                                                   3/      ___\  x                                                                                                                                                                                                                                                                                                                                                                                   3  x                                                                                                                                                                                                                                                                                                                                                                                2  x    /      ___\                                                                                                                                                                                                                                                                                                                                                                              2/      ___\  x                                                                                                                                                                                                                                                                                                                                                                            x    /      ___\                                                                                                                                                                                
 |      E                                                                                                                                                                                                    log \E - \/ 2 /*e                                                                                                                                                                                                                                                                                                                                                                                 pi *e                                                                                                                                                                                                                                                                                                                                                                                 log \E - \/ 2 /*e                                                                                                                                                                                                                                                                                                                                                                                I*pi *e                                                                                                                                                                                                                                                                                                                                                                             3*pi *e *log\E - \/ 2 /                                                                                                                                                                                                                                                                                                                                                                    3*pi*I*log \E - \/ 2 /*e                                                                                                                                                                                                                                                                                                                                                                     2*pi*I*e *log\E - \/ 2 /                                                                                                                                                                                
 | ------------ dx = C + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
 |            x                         x              x                              x                                  x                x                                    x                                      x                    x                                    x                                      x                                    x                                    x                                  x              x                              x                                  x                x                                    x                                      x                    x                                    x                                      x                                    x                                    x                                  x              x                              x                                  x                x                                    x                                      x                    x                                    x                                      x                                    x                                    x                                  x              x                              x                                  x                x                                    x                                      x                    x                                    x                                      x                                    x                                    x                                  x              x                              x                                  x                x                                    x                                      x                    x                                    x                                      x                                    x                                    x                                  x              x                              x                                  x                x                                    x                                      x                    x                                    x                                      x                                    x                                    x                                  x              x                              x                                  x                x                                    x                                      x                    x                                    x                                      x                                    x                                    x                
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 | \\/ 2  - E/           pi *\\/ 2  - E/  + \\/ 2  - E/ *log \E - \/ 2 / + \\/ 2  - E/ *log \E - \/ 2 / - pi *\\/ 2  - E/  - 2*\\/ 2  - E/ *log \E - \/ 2 / - 6*pi *\\/ 2  - E/ *log \E - \/ 2 / + 2*I*pi *\\/ 2  - E/  + 6*pi *\\/ 2  - E/ *log\E - \/ 2 / - 6*pi*I*\\/ 2  - E/ *log \E - \/ 2 / - 4*I*pi *\\/ 2  - E/ *log\E - \/ 2 / + 2*pi*I*\\/ 2  - E/ *log\E - \/ 2 / + 4*pi*I*\\/ 2  - E/ *log \E - \/ 2 /   pi *\\/ 2  - E/  + \\/ 2  - E/ *log \E - \/ 2 / + \\/ 2  - E/ *log \E - \/ 2 / - pi *\\/ 2  - E/  - 2*\\/ 2  - E/ *log \E - \/ 2 / - 6*pi *\\/ 2  - E/ *log \E - \/ 2 / + 2*I*pi *\\/ 2  - E/  + 6*pi *\\/ 2  - E/ *log\E - \/ 2 / - 6*pi*I*\\/ 2  - E/ *log \E - \/ 2 / - 4*I*pi *\\/ 2  - E/ *log\E - \/ 2 / + 2*pi*I*\\/ 2  - E/ *log\E - \/ 2 / + 4*pi*I*\\/ 2  - E/ *log \E - \/ 2 /   pi *\\/ 2  - E/  + \\/ 2  - E/ *log \E - \/ 2 / + \\/ 2  - E/ *log \E - \/ 2 / - pi *\\/ 2  - E/  - 2*\\/ 2  - E/ *log \E - \/ 2 / - 6*pi *\\/ 2  - E/ *log \E - \/ 2 / + 2*I*pi *\\/ 2  - E/  + 6*pi *\\/ 2  - E/ *log\E - \/ 2 / - 6*pi*I*\\/ 2  - E/ *log \E - \/ 2 / - 4*I*pi *\\/ 2  - E/ *log\E - \/ 2 / + 2*pi*I*\\/ 2  - E/ *log\E - \/ 2 / + 4*pi*I*\\/ 2  - E/ *log \E - \/ 2 /   pi *\\/ 2  - E/  + \\/ 2  - E/ *log \E - \/ 2 / + \\/ 2  - E/ *log \E - \/ 2 / - pi *\\/ 2  - E/  - 2*\\/ 2  - E/ *log \E - \/ 2 / - 6*pi *\\/ 2  - E/ *log \E - \/ 2 / + 2*I*pi *\\/ 2  - E/  + 6*pi *\\/ 2  - E/ *log\E - \/ 2 / - 6*pi*I*\\/ 2  - E/ *log \E - \/ 2 / - 4*I*pi *\\/ 2  - E/ *log\E - \/ 2 / + 2*pi*I*\\/ 2  - E/ *log\E - \/ 2 / + 4*pi*I*\\/ 2  - E/ *log \E - \/ 2 /   pi *\\/ 2  - E/  + \\/ 2  - E/ *log \E - \/ 2 / + \\/ 2  - E/ *log \E - \/ 2 / - pi *\\/ 2  - E/  - 2*\\/ 2  - E/ *log \E - \/ 2 / - 6*pi *\\/ 2  - E/ *log \E - \/ 2 / + 2*I*pi *\\/ 2  - E/  + 6*pi *\\/ 2  - E/ *log\E - \/ 2 / - 6*pi*I*\\/ 2  - E/ *log \E - \/ 2 / - 4*I*pi *\\/ 2  - E/ *log\E - \/ 2 / + 2*pi*I*\\/ 2  - E/ *log\E - \/ 2 / + 4*pi*I*\\/ 2  - E/ *log \E - \/ 2 /   pi *\\/ 2  - E/  + \\/ 2  - E/ *log \E - \/ 2 / + \\/ 2  - E/ *log \E - \/ 2 / - pi *\\/ 2  - E/  - 2*\\/ 2  - E/ *log \E - \/ 2 / - 6*pi *\\/ 2  - E/ *log \E - \/ 2 / + 2*I*pi *\\/ 2  - E/  + 6*pi *\\/ 2  - E/ *log\E - \/ 2 / - 6*pi*I*\\/ 2  - E/ *log \E - \/ 2 / - 4*I*pi *\\/ 2  - E/ *log\E - \/ 2 / + 2*pi*I*\\/ 2  - E/ *log\E - \/ 2 / + 4*pi*I*\\/ 2  - E/ *log \E - \/ 2 /   pi *\\/ 2  - E/  + \\/ 2  - E/ *log \E - \/ 2 / + \\/ 2  - E/ *log \E - \/ 2 / - pi *\\/ 2  - E/  - 2*\\/ 2  - E/ *log \E - \/ 2 / - 6*pi *\\/ 2  - E/ *log \E - \/ 2 / + 2*I*pi *\\/ 2  - E/  + 6*pi *\\/ 2  - E/ *log\E - \/ 2 / - 6*pi*I*\\/ 2  - E/ *log \E - \/ 2 / - 4*I*pi *\\/ 2  - E/ *log\E - \/ 2 / + 2*pi*I*\\/ 2  - E/ *log\E - \/ 2 / + 4*pi*I*\\/ 2  - E/ *log \E - \/ 2 /
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∫ex(−e+2)x dx=C−π2ex−π2(−e+2)x−6π2(−e+2)xlog⁡(e−2)2−2(−e+2)xlog⁡(e−2)3+(−e+2)xlog⁡(e−2)4+(−e+2)xlog⁡(e−2)2+6π2(−e+2)xlog⁡(e−2)+π4(−e+2)x−4iπ3(−e+2)xlog⁡(e−2)−6iπ(−e+2)xlog⁡(e−2)2+4iπ(−e+2)xlog⁡(e−2)3+2iπ(−e+2)xlog⁡(e−2)+2iπ3(−e+2)x−exlog⁡(e−2)3−π2(−e+2)x−6π2(−e+2)xlog⁡(e−2)2−2(−e+2)xlog⁡(e−2)3+(−e+2)xlog⁡(e−2)4+(−e+2)xlog⁡(e−2)2+6π2(−e+2)xlog⁡(e−2)+π4(−e+2)x−4iπ3(−e+2)xlog⁡(e−2)−6iπ(−e+2)xlog⁡(e−2)2+4iπ(−e+2)xlog⁡(e−2)3+2iπ(−e+2)xlog⁡(e−2)+2iπ3(−e+2)x+exlog⁡(e−2)2−π2(−e+2)x−6π2(−e+2)xlog⁡(e−2)2−2(−e+2)xlog⁡(e−2)3+(−e+2)xlog⁡(e−2)4+(−e+2)xlog⁡(e−2)2+6π2(−e+2)xlog⁡(e−2)+π4(−e+2)x−4iπ3(−e+2)xlog⁡(e−2)−6iπ(−e+2)xlog⁡(e−2)2+4iπ(−e+2)xlog⁡(e−2)3+2iπ(−e+2)xlog⁡(e−2)+2iπ3(−e+2)x+3π2exlog⁡(e−2)−π2(−e+2)x−6π2(−e+2)xlog⁡(e−2)2−2(−e+2)xlog⁡(e−2)3+(−e+2)xlog⁡(e−2)4+(−e+2)xlog⁡(e−2)2+6π2(−e+2)xlog⁡(e−2)+π4(−e+2)x−4iπ3(−e+2)xlog⁡(e−2)−6iπ(−e+2)xlog⁡(e−2)2+4iπ(−e+2)xlog⁡(e−2)3+2iπ(−e+2)xlog⁡(e−2)+2iπ3(−e+2)x−3iπexlog⁡(e−2)2−π2(−e+2)x−6π2(−e+2)xlog⁡(e−2)2−2(−e+2)xlog⁡(e−2)3+(−e+2)xlog⁡(e−2)4+(−e+2)xlog⁡(e−2)2+6π2(−e+2)xlog⁡(e−2)+π4(−e+2)x−4iπ3(−e+2)xlog⁡(e−2)−6iπ(−e+2)xlog⁡(e−2)2+4iπ(−e+2)xlog⁡(e−2)3+2iπ(−e+2)xlog⁡(e−2)+2iπ3(−e+2)x+2iπexlog⁡(e−2)−π2(−e+2)x−6π2(−e+2)xlog⁡(e−2)2−2(−e+2)xlog⁡(e−2)3+(−e+2)xlog⁡(e−2)4+(−e+2)xlog⁡(e−2)2+6π2(−e+2)xlog⁡(e−2)+π4(−e+2)x−4iπ3(−e+2)xlog⁡(e−2)−6iπ(−e+2)xlog⁡(e−2)2+4iπ(−e+2)xlog⁡(e−2)3+2iπ(−e+2)xlog⁡(e−2)+2iπ3(−e+2)x+iπ3ex−π2(−e+2)x−6π2(−e+2)xlog⁡(e−2)2−2(−e+2)xlog⁡(e−2)3+(−e+2)xlog⁡(e−2)4+(−e+2)xlog⁡(e−2)2+6π2(−e+2)xlog⁡(e−2)+π4(−e+2)x−4iπ3(−e+2)xlog⁡(e−2)−6iπ(−e+2)xlog⁡(e−2)2+4iπ(−e+2)xlog⁡(e−2)3+2iπ(−e+2)xlog⁡(e−2)+2iπ3(−e+2)x\int \frac{e^{x}}{\left(- e + \sqrt{2}\right)^{x}}\, dx = C - \frac{\pi^{2} e^{x}}{- \pi^{2} \left(- e + \sqrt{2}\right)^{x} - 6 \pi^{2} \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{2} - 2 \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{3} + \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{4} + \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{2} + 6 \pi^{2} \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)} + \pi^{4} \left(- e + \sqrt{2}\right)^{x} - 4 i \pi^{3} \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)} - 6 i \pi \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{2} + 4 i \pi \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{3} + 2 i \pi \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)} + 2 i \pi^{3} \left(- e + \sqrt{2}\right)^{x}} - \frac{e^{x} \log{\left(e - \sqrt{2} \right)}^{3}}{- \pi^{2} \left(- e + \sqrt{2}\right)^{x} - 6 \pi^{2} \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{2} - 2 \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{3} + \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{4} + \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{2} + 6 \pi^{2} \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)} + \pi^{4} \left(- e + \sqrt{2}\right)^{x} - 4 i \pi^{3} \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)} - 6 i \pi \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{2} + 4 i \pi \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{3} + 2 i \pi \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)} + 2 i \pi^{3} \left(- e + \sqrt{2}\right)^{x}} + \frac{e^{x} \log{\left(e - \sqrt{2} \right)}^{2}}{- \pi^{2} \left(- e + \sqrt{2}\right)^{x} - 6 \pi^{2} \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{2} - 2 \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{3} + \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{4} + \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{2} + 6 \pi^{2} \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)} + \pi^{4} \left(- e + \sqrt{2}\right)^{x} - 4 i \pi^{3} \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)} - 6 i \pi \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{2} + 4 i \pi \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{3} + 2 i \pi \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)} + 2 i \pi^{3} \left(- e + \sqrt{2}\right)^{x}} + \frac{3 \pi^{2} e^{x} \log{\left(e - \sqrt{2} \right)}}{- \pi^{2} \left(- e + \sqrt{2}\right)^{x} - 6 \pi^{2} \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{2} - 2 \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{3} + \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{4} + \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{2} + 6 \pi^{2} \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)} + \pi^{4} \left(- e + \sqrt{2}\right)^{x} - 4 i \pi^{3} \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)} - 6 i \pi \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{2} + 4 i \pi \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{3} + 2 i \pi \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)} + 2 i \pi^{3} \left(- e + \sqrt{2}\right)^{x}} - \frac{3 i \pi e^{x} \log{\left(e - \sqrt{2} \right)}^{2}}{- \pi^{2} \left(- e + \sqrt{2}\right)^{x} - 6 \pi^{2} \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{2} - 2 \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{3} + \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{4} + \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{2} + 6 \pi^{2} \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)} + \pi^{4} \left(- e + \sqrt{2}\right)^{x} - 4 i \pi^{3} \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)} - 6 i \pi \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{2} + 4 i \pi \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{3} + 2 i \pi \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)} + 2 i \pi^{3} \left(- e + \sqrt{2}\right)^{x}} + \frac{2 i \pi e^{x} \log{\left(e - \sqrt{2} \right)}}{- \pi^{2} \left(- e + \sqrt{2}\right)^{x} - 6 \pi^{2} \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{2} - 2 \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{3} + \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{4} + \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{2} + 6 \pi^{2} \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)} + \pi^{4} \left(- e + \sqrt{2}\right)^{x} - 4 i \pi^{3} \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)} - 6 i \pi \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{2} + 4 i \pi \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{3} + 2 i \pi \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)} + 2 i \pi^{3} \left(- e + \sqrt{2}\right)^{x}} + \frac{i \pi^{3} e^{x}}{- \pi^{2} \left(- e + \sqrt{2}\right)^{x} - 6 \pi^{2} \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{2} - 2 \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{3} + \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{4} + \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{2} + 6 \pi^{2} \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)} + \pi^{4} \left(- e + \sqrt{2}\right)^{x} - 4 i \pi^{3} \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)} - 6 i \pi \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{2} + 4 i \pi \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)}^{3} + 2 i \pi \left(- e + \sqrt{2}\right)^{x} \log{\left(e - \sqrt{2} \right)} + 2 i \pi^{3} \left(- e + \sqrt{2}\right)^{x}}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.905-5
Trazar el gráfico f(x)
Respuesta numérica [src] 
(-0.217652826919496 - 0.93092730864142j)
(-0.217652826919496 - 0.93092730864142j)

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

    © Sr Examen – Калькулятор