Sr Examen
Integral de 4^(x/3)8cos(nx) dx
Solución
Ha introducido
[src]
pi / | | x | - | 3 | 4 *8*cos(n*x) dx | / 0
$$\int\limits_{0}^{\pi} 8 \cdot 4^{\frac{x}{3}} \cos{\left(n x \right)}\, dx$$
Integral((4^(x/3)*8)*cos(n*x), (x, 0, pi))
Respuesta (Indefinida)
[src]
/ | x x | x - - | - 3 3 | 3 48*4 *cos(n*x)*log(2) 72*n*4 *sin(n*x) | 4 *8*cos(n*x) dx = C + --------------------- + ---------------- | 2 2 2 2 / 4*log (2) + 9*n 4*log (2) + 9*n
$$\int 8 \cdot 4^{\frac{x}{3}} \cos{\left(n x \right)}\, dx = \frac{72 \cdot 4^{\frac{x}{3}} n \sin{\left(n x \right)}}{9 n^{2} + 4 \log{\left(2 \right)}^{2}} + \frac{48 \cdot 4^{\frac{x}{3}} \log{\left(2 \right)} \cos{\left(n x \right)}}{9 n^{2} + 4 \log{\left(2 \right)}^{2}} + C$$
Respuesta
[src]
pi pi
-- --
3 3
48*log(2) 48*4 *cos(pi*n)*log(2) 72*n*4 *sin(pi*n)
- ---------------- + ----------------------- + ------------------
2 2 2 2 2 2
4*log (2) + 9*n 4*log (2) + 9*n 4*log (2) + 9*n
$$\frac{72 \cdot 4^{\frac{\pi}{3}} n \sin{\left(\pi n \right)}}{9 n^{2} + 4 \log{\left(2 \right)}^{2}} + \frac{48 \cdot 4^{\frac{\pi}{3}} \log{\left(2 \right)} \cos{\left(\pi n \right)}}{9 n^{2} + 4 \log{\left(2 \right)}^{2}} - \frac{48 \log{\left(2 \right)}}{9 n^{2} + 4 \log{\left(2 \right)}^{2}}$$
=
=
pi pi
-- --
3 3
48*log(2) 48*4 *cos(pi*n)*log(2) 72*n*4 *sin(pi*n)
- ---------------- + ----------------------- + ------------------
2 2 2 2 2 2
4*log (2) + 9*n 4*log (2) + 9*n 4*log (2) + 9*n
$$\frac{72 \cdot 4^{\frac{\pi}{3}} n \sin{\left(\pi n \right)}}{9 n^{2} + 4 \log{\left(2 \right)}^{2}} + \frac{48 \cdot 4^{\frac{\pi}{3}} \log{\left(2 \right)} \cos{\left(\pi n \right)}}{9 n^{2} + 4 \log{\left(2 \right)}^{2}} - \frac{48 \log{\left(2 \right)}}{9 n^{2} + 4 \log{\left(2 \right)}^{2}}$$
-48*log(2)/(4*log(2)^2 + 9*n^2) + 48*4^(pi/3)*cos(pi*n)*log(2)/(4*log(2)^2 + 9*n^2) + 72*n*4^(pi/3)*sin(pi*n)/(4*log(2)^2 + 9*n^2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.