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