Sr Examen
Integral de 3^xsen(3x) dx
Solución
Ha introducido
[src]
1 / | | x | 3 *sin(3*x) dx | / 0
$$\int\limits_{0}^{1} 3^{x} \sin{\left(3 x \right)}\, dx$$
Integral(3^x*sin(3*x), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | x x | x 3*3 *cos(3*x) 3 *log(3)*sin(3*x) | 3 *sin(3*x) dx = C - ------------- + ------------------ | 2 2 / 9 + log (3) 9 + log (3)
$$\int 3^{x} \sin{\left(3 x \right)}\, dx = \frac{3^{x} \log{\left(3 \right)} \sin{\left(3 x \right)}}{\log{\left(3 \right)}^{2} + 9} - \frac{3 \cdot 3^{x} \cos{\left(3 x \right)}}{\log{\left(3 \right)}^{2} + 9} + C$$
Gráfica
Respuesta
[src]
3 9*cos(3) 3*log(3)*sin(3)
----------- - ----------- + ---------------
2 2 2
9 + log (3) 9 + log (3) 9 + log (3)
$$\frac{3 \log{\left(3 \right)} \sin{\left(3 \right)}}{\log{\left(3 \right)}^{2} + 9} + \frac{3}{\log{\left(3 \right)}^{2} + 9} - \frac{9 \cos{\left(3 \right)}}{\log{\left(3 \right)}^{2} + 9}$$
=
=
3 9*cos(3) 3*log(3)*sin(3)
----------- - ----------- + ---------------
2 2 2
9 + log (3) 9 + log (3) 9 + log (3)
$$\frac{3 \log{\left(3 \right)} \sin{\left(3 \right)}}{\log{\left(3 \right)}^{2} + 9} + \frac{3}{\log{\left(3 \right)}^{2} + 9} - \frac{9 \cos{\left(3 \right)}}{\log{\left(3 \right)}^{2} + 9}$$
3/(9 + log(3)^2) - 9*cos(3)/(9 + log(3)^2) + 3*log(3)*sin(3)/(9 + log(3)^2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.