Sr Examen
Integral de e^x*dx/(sqrt(2)-e)^x dx
Solución
Ha introducido
[src]
1 / | | x | E | ------------ dx | x | / ___ \ | \\/ 2 - E/ | / 0
$$\int\limits_{0}^{1} \frac{e^{x}}{\left(- e + \sqrt{2}\right)^{x}}\, dx$$
Integral(E^x/(sqrt(2) - E)^x, (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | | 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 | / ___ \ 4 / ___ \ / ___ \ 2/ ___\ / ___ \ 4/ ___\ 2 / ___ \ / ___ \ 3/ ___\ 2 / ___ \ 2/ ___\ 3 / ___ \ 2 / ___ \ / ___\ / ___ \ 2/ ___\ 3 / ___ \ / ___\ / ___ \ / ___\ / ___ \ 3/ ___\ 4 / ___ \ / ___ \ 2/ ___\ / ___ \ 4/ ___\ 2 / ___ \ / ___ \ 3/ ___\ 2 / ___ \ 2/ ___\ 3 / ___ \ 2 / ___ \ / ___\ / ___ \ 2/ ___\ 3 / ___ \ / ___\ / ___ \ / ___\ / ___ \ 3/ ___\ 4 / ___ \ / ___ \ 2/ ___\ / ___ \ 4/ ___\ 2 / ___ \ / ___ \ 3/ ___\ 2 / ___ \ 2/ ___\ 3 / ___ \ 2 / ___ \ / ___\ / ___ \ 2/ ___\ 3 / ___ \ / ___\ / ___ \ / ___\ / ___ \ 3/ ___\ 4 / ___ \ / ___ \ 2/ ___\ / ___ \ 4/ ___\ 2 / ___ \ / ___ \ 3/ ___\ 2 / ___ \ 2/ ___\ 3 / ___ \ 2 / ___ \ / ___\ / ___ \ 2/ ___\ 3 / ___ \ / ___\ / ___ \ / ___\ / ___ \ 3/ ___\ 4 / ___ \ / ___ \ 2/ ___\ / ___ \ 4/ ___\ 2 / ___ \ / ___ \ 3/ ___\ 2 / ___ \ 2/ ___\ 3 / ___ \ 2 / ___ \ / ___\ / ___ \ 2/ ___\ 3 / ___ \ / ___\ / ___ \ / ___\ / ___ \ 3/ ___\ 4 / ___ \ / ___ \ 2/ ___\ / ___ \ 4/ ___\ 2 / ___ \ / ___ \ 3/ ___\ 2 / ___ \ 2/ ___\ 3 / ___ \ 2 / ___ \ / ___\ / ___ \ 2/ ___\ 3 / ___ \ / ___\ / ___ \ / ___\ / ___ \ 3/ ___\ 4 / ___ \ / ___ \ 2/ ___\ / ___ \ 4/ ___\ 2 / ___ \ / ___ \ 3/ ___\ 2 / ___ \ 2/ ___\ 3 / ___ \ 2 / ___ \ / ___\ / ___ \ 2/ ___\ 3 / ___ \ / ___\ / ___ \ / ___\ / ___ \ 3/ ___\ | \\/ 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 / | /
$$\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}}$$
Gráfica
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.