Sr Examen
Integral de e^x*cosnx dx
Solución
Ha introducido
[src]
157 --- 50 / | | x | E *cos(n*x) dx | / -157 ----- 50
$$\int\limits_{- \frac{157}{50}}^{\frac{157}{50}} e^{x} \cos{\left(n x \right)}\, dx$$
Integral(E^x*cos(n*x), (x, -157/50, 157/50))
Respuesta (Indefinida)
[src]
/ | x x | x cos(n*x)*e n*e *sin(n*x) | E *cos(n*x) dx = C + ----------- + ------------- | 2 2 / 1 + n 1 + n
$$\int e^{x} \cos{\left(n x \right)}\, dx = C + \frac{n e^{x} \sin{\left(n x \right)}}{n^{2} + 1} + \frac{e^{x} \cos{\left(n x \right)}}{n^{2} + 1}$$
Respuesta
[src]
157 -157 -157 157
--- ----- ----- ---
/157*n\ 50 /157*n\ 50 50 /157*n\ 50 /157*n\
cos|-----|*e cos|-----|*e n*e *sin|-----| n*e *sin|-----|
\ 50 / \ 50 / \ 50 / \ 50 /
--------------- - ----------------- + ------------------- + -----------------
2 2 2 2
1 + n 1 + n 1 + n 1 + n
$$\frac{n \sin{\left(\frac{157 n}{50} \right)}}{\left(n^{2} + 1\right) e^{\frac{157}{50}}} + \frac{n e^{\frac{157}{50}} \sin{\left(\frac{157 n}{50} \right)}}{n^{2} + 1} - \frac{\cos{\left(\frac{157 n}{50} \right)}}{\left(n^{2} + 1\right) e^{\frac{157}{50}}} + \frac{e^{\frac{157}{50}} \cos{\left(\frac{157 n}{50} \right)}}{n^{2} + 1}$$
=
=
157 -157 -157 157
--- ----- ----- ---
/157*n\ 50 /157*n\ 50 50 /157*n\ 50 /157*n\
cos|-----|*e cos|-----|*e n*e *sin|-----| n*e *sin|-----|
\ 50 / \ 50 / \ 50 / \ 50 /
--------------- - ----------------- + ------------------- + -----------------
2 2 2 2
1 + n 1 + n 1 + n 1 + n
$$\frac{n \sin{\left(\frac{157 n}{50} \right)}}{\left(n^{2} + 1\right) e^{\frac{157}{50}}} + \frac{n e^{\frac{157}{50}} \sin{\left(\frac{157 n}{50} \right)}}{n^{2} + 1} - \frac{\cos{\left(\frac{157 n}{50} \right)}}{\left(n^{2} + 1\right) e^{\frac{157}{50}}} + \frac{e^{\frac{157}{50}} \cos{\left(\frac{157 n}{50} \right)}}{n^{2} + 1}$$
cos(157*n/50)*exp(157/50)/(1 + n^2) - cos(157*n/50)*exp(-157/50)/(1 + n^2) + n*exp(-157/50)*sin(157*n/50)/(1 + n^2) + n*exp(157/50)*sin(157*n/50)/(1 + n^2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.