Sr Examen
Integral de ((2^x)/(log(2)/log(10)))*(-3*sin(3x)) dx
Solución
Ha introducido
[src]
1 / | | x | 2 | ---------*-3*sin(3*x) dx | / log(2)\ | |-------| | \log(10)/ | / 0
$$\int\limits_{0}^{1} \frac{2^{x}}{\log{\left(2 \right)} \frac{1}{\log{\left(10 \right)}}} \left(- 3 \sin{\left(3 x \right)}\right)\, dx$$
Integral((2^x/((log(2)/log(10))))*(-3*sin(3*x)), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ x x \ / | 3*2 *cos(3*x) 2 *log(2)*sin(3*x)| | 3*|- ------------- + ------------------|*log(10) | x | 2 2 | | 2 \ 9 + log (2) 9 + log (2) / | ---------*-3*sin(3*x) dx = C - ------------------------------------------------ | / log(2)\ log(2) | |-------| | \log(10)/ | /
$$\int \frac{2^{x}}{\log{\left(2 \right)} \frac{1}{\log{\left(10 \right)}}} \left(- 3 \sin{\left(3 x \right)}\right)\, dx = C - \frac{3 \left(\frac{2^{x} \log{\left(2 \right)} \sin{\left(3 x \right)}}{\log{\left(2 \right)}^{2} + 9} - \frac{3 \cdot 2^{x} \cos{\left(3 x \right)}}{\log{\left(2 \right)}^{2} + 9}\right) \log{\left(10 \right)}}{\log{\left(2 \right)}}$$
Gráfica
Respuesta
[src]
/ 6*cos(3) 2*log(2)*sin(3)\
3*|- ----------- + ---------------|*log(10)
| 2 2 |
9*log(10) \ 9 + log (2) 9 + log (2) /
- -------------------- - -------------------------------------------
/ 2 \ log(2)
\9 + log (2)/*log(2)
$$- \frac{3 \left(\frac{2 \log{\left(2 \right)} \sin{\left(3 \right)}}{\log{\left(2 \right)}^{2} + 9} - \frac{6 \cos{\left(3 \right)}}{\log{\left(2 \right)}^{2} + 9}\right) \log{\left(10 \right)}}{\log{\left(2 \right)}} - \frac{9 \log{\left(10 \right)}}{\left(\log{\left(2 \right)}^{2} + 9\right) \log{\left(2 \right)}}$$
=
=
/ 6*cos(3) 2*log(2)*sin(3)\
3*|- ----------- + ---------------|*log(10)
| 2 2 |
9*log(10) \ 9 + log (2) 9 + log (2) /
- -------------------- - -------------------------------------------
/ 2 \ log(2)
\9 + log (2)/*log(2)
$$- \frac{3 \left(\frac{2 \log{\left(2 \right)} \sin{\left(3 \right)}}{\log{\left(2 \right)}^{2} + 9} - \frac{6 \cos{\left(3 \right)}}{\log{\left(2 \right)}^{2} + 9}\right) \log{\left(10 \right)}}{\log{\left(2 \right)}} - \frac{9 \log{\left(10 \right)}}{\left(\log{\left(2 \right)}^{2} + 9\right) \log{\left(2 \right)}}$$
-9*log(10)/((9 + log(2)^2)*log(2)) - 3*(-6*cos(3)/(9 + log(2)^2) + 2*log(2)*sin(3)/(9 + log(2)^2))*log(10)/log(2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.