Sr Examen
Integral de (2^x)*cosx dx
Solución
Ha introducido
[src]
1 / | | x | 2 *cos(x) dx | / 0
$$\int\limits_{0}^{1} 2^{x} \cos{\left(x \right)}\, dx$$
Integral(2^x*cos(x), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | x x | x 2 *sin(x) 2 *cos(x)*log(2) | 2 *cos(x) dx = C + ----------- + ---------------- | 2 2 / 1 + log (2) 1 + log (2)
$$\int 2^{x} \cos{\left(x \right)}\, dx = \frac{2^{x} \sin{\left(x \right)}}{\log{\left(2 \right)}^{2} + 1} + \frac{2^{x} \log{\left(2 \right)} \cos{\left(x \right)}}{\log{\left(2 \right)}^{2} + 1} + C$$
Gráfica
Respuesta
[src]
log(2) 2*sin(1) 2*cos(1)*log(2)
- ----------- + ----------- + ---------------
2 2 2
1 + log (2) 1 + log (2) 1 + log (2)
$$- \frac{\log{\left(2 \right)}}{\log{\left(2 \right)}^{2} + 1} + \frac{2 \log{\left(2 \right)} \cos{\left(1 \right)}}{\log{\left(2 \right)}^{2} + 1} + \frac{2 \sin{\left(1 \right)}}{\log{\left(2 \right)}^{2} + 1}$$
=
=
log(2) 2*sin(1) 2*cos(1)*log(2)
- ----------- + ----------- + ---------------
2 2 2
1 + log (2) 1 + log (2) 1 + log (2)
$$- \frac{\log{\left(2 \right)}}{\log{\left(2 \right)}^{2} + 1} + \frac{2 \log{\left(2 \right)} \cos{\left(1 \right)}}{\log{\left(2 \right)}^{2} + 1} + \frac{2 \sin{\left(1 \right)}}{\log{\left(2 \right)}^{2} + 1}$$
-log(2)/(1 + log(2)^2) + 2*sin(1)/(1 + log(2)^2) + 2*cos(1)*log(2)/(1 + log(2)^2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.