Sr Examen
Integral de 5^x*cos(6x) dx
Solución
Ha introducido
[src]
1 / | | x | 5 *cos(6*x) dx | / 0
$$\int\limits_{0}^{1} 5^{x} \cos{\left(6 x \right)}\, dx$$
Integral(5^x*cos(6*x), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | x x | x 6*5 *sin(6*x) 5 *cos(6*x)*log(5) | 5 *cos(6*x) dx = C + ------------- + ------------------ | 2 2 / 36 + log (5) 36 + log (5)
$$\int 5^{x} \cos{\left(6 x \right)}\, dx = \frac{6 \cdot 5^{x} \sin{\left(6 x \right)}}{\log{\left(5 \right)}^{2} + 36} + \frac{5^{x} \log{\left(5 \right)} \cos{\left(6 x \right)}}{\log{\left(5 \right)}^{2} + 36} + C$$
Gráfica
Respuesta
[src]
log(5) 30*sin(6) 5*cos(6)*log(5)
- ------------ + ------------ + ---------------
2 2 2
36 + log (5) 36 + log (5) 36 + log (5)
$$\frac{30 \sin{\left(6 \right)}}{\log{\left(5 \right)}^{2} + 36} - \frac{\log{\left(5 \right)}}{\log{\left(5 \right)}^{2} + 36} + \frac{5 \log{\left(5 \right)} \cos{\left(6 \right)}}{\log{\left(5 \right)}^{2} + 36}$$
=
=
log(5) 30*sin(6) 5*cos(6)*log(5)
- ------------ + ------------ + ---------------
2 2 2
36 + log (5) 36 + log (5) 36 + log (5)
$$\frac{30 \sin{\left(6 \right)}}{\log{\left(5 \right)}^{2} + 36} - \frac{\log{\left(5 \right)}}{\log{\left(5 \right)}^{2} + 36} + \frac{5 \log{\left(5 \right)} \cos{\left(6 \right)}}{\log{\left(5 \right)}^{2} + 36}$$
-log(5)/(36 + log(5)^2) + 30*sin(6)/(36 + log(5)^2) + 5*cos(6)*log(5)/(36 + log(5)^2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.