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