Sr Examen
Integral de 5^(2x)*cos(5x) dx
Solución
Ha introducido
[src]
1 / | | 2*x | 5 *cos(5*x) dx | / 0
$$\int\limits_{0}^{1} 5^{2 x} \cos{\left(5 x \right)}\, dx$$
Integral(5^(2*x)*cos(5*x), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | 2*x 2*x | 2*x 5*5 *sin(5*x) 2*5 *cos(5*x)*log(5) | 5 *cos(5*x) dx = C + --------------- + ---------------------- | 2 2 / 25 + 4*log (5) 25 + 4*log (5)
$$\int 5^{2 x} \cos{\left(5 x \right)}\, dx = \frac{5 \cdot 5^{2 x} \sin{\left(5 x \right)}}{4 \log{\left(5 \right)}^{2} + 25} + \frac{2 \cdot 5^{2 x} \log{\left(5 \right)} \cos{\left(5 x \right)}}{4 \log{\left(5 \right)}^{2} + 25} + C$$
Gráfica
Respuesta
[src]
2*log(5) 125*sin(5) 50*cos(5)*log(5)
- -------------- + -------------- + ----------------
2 2 2
25 + 4*log (5) 25 + 4*log (5) 25 + 4*log (5)
$$\frac{125 \sin{\left(5 \right)}}{4 \log{\left(5 \right)}^{2} + 25} - \frac{2 \log{\left(5 \right)}}{4 \log{\left(5 \right)}^{2} + 25} + \frac{50 \log{\left(5 \right)} \cos{\left(5 \right)}}{4 \log{\left(5 \right)}^{2} + 25}$$
=
=
2*log(5) 125*sin(5) 50*cos(5)*log(5)
- -------------- + -------------- + ----------------
2 2 2
25 + 4*log (5) 25 + 4*log (5) 25 + 4*log (5)
$$\frac{125 \sin{\left(5 \right)}}{4 \log{\left(5 \right)}^{2} + 25} - \frac{2 \log{\left(5 \right)}}{4 \log{\left(5 \right)}^{2} + 25} + \frac{50 \log{\left(5 \right)} \cos{\left(5 \right)}}{4 \log{\left(5 \right)}^{2} + 25}$$
-2*log(5)/(25 + 4*log(5)^2) + 125*sin(5)/(25 + 4*log(5)^2) + 50*cos(5)*log(5)/(25 + 4*log(5)^2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.