Sr Examen
Integral de (5tan(x)-2)/(2sin(2x)+5) dx
Solución
Ha introducido
[src]
pi -- 4 / | | 5*tan(x) - 2 | -------------- dx | 2*sin(2*x) + 5 | / 0
$$\int\limits_{0}^{\frac{\pi}{4}} \frac{5 \tan{\left(x \right)} - 2}{2 \sin{\left(2 x \right)} + 5}\, dx$$
Integral((5*tan(x) - 2)/(2*sin(2*x) + 5), (x, 0, pi/4))
Respuesta (Indefinida)
[src]
/ / pi\ \
| |x - --| / ____ ____ \|
/ / ____ | | 2 | |2*\/ 21 5*\/ 21 *tan(x)||
| | 2*\/ 21 *|pi*floor|------| + atan|-------- + ---------------||
| 5*tan(x) - 2 | tan(x) \ \ pi / \ 21 21 //
| -------------- dx = C + 5* | -------------- dx - --------------------------------------------------------------
| 2*sin(2*x) + 5 | 5 + 2*sin(2*x) 21
| |
/ /
$$\int \frac{5 \tan{\left(x \right)} - 2}{2 \sin{\left(2 x \right)} + 5}\, dx = C - \frac{2 \sqrt{21} \left(\operatorname{atan}{\left(\frac{5 \sqrt{21} \tan{\left(x \right)}}{21} + \frac{2 \sqrt{21}}{21} \right)} + \pi \left\lfloor{\frac{x - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{21} + 5 \int \frac{\tan{\left(x \right)}}{2 \sin{\left(2 x \right)} + 5}\, dx$$
Respuesta
[src]
pi -- 4 / | | -2 + 5*tan(x) | -------------- dx | 5 + 2*sin(2*x) | / 0
$$\int\limits_{0}^{\frac{\pi}{4}} \frac{5 \tan{\left(x \right)} - 2}{2 \sin{\left(2 x \right)} + 5}\, dx$$
=
=
pi -- 4 / | | -2 + 5*tan(x) | -------------- dx | 5 + 2*sin(2*x) | / 0
$$\int\limits_{0}^{\frac{\pi}{4}} \frac{5 \tan{\left(x \right)} - 2}{2 \sin{\left(2 x \right)} + 5}\, dx$$
Integral((-2 + 5*tan(x))/(5 + 2*sin(2*x)), (x, 0, pi/4))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.