Sr Examen
Integral de (2tgx+3)/(sin^2x+2cos^2x) dx
Solución
Ha introducido
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1 / | | 2*tan(x) + 3 | ------------------- dx | 2 2 | sin (x) + 2*cos (x) | / 0
$$\int\limits_{0}^{1} \frac{2 \tan{\left(x \right)} + 3}{\sin^{2}{\left(x \right)} + 2 \cos^{2}{\left(x \right)}}\, dx$$
Integral((2*tan(x) + 3)/(sin(x)^2 + 2*cos(x)^2), (x, 0, 1))
Respuesta (Indefinida)
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/ /x pi\ \ / /x pi\ \
| |- - --| | | |- - --| |
/ / ___ | |2 2 | / ___ /x\\| ___ | |2 2 | / ___ /x\\|
| | 3*\/ 2 *|pi*floor|------| + atan|1 + \/ 2 *tan|-||| 3*\/ 2 *|pi*floor|------| + atan|-1 + \/ 2 *tan|-|||
| 2*tan(x) + 3 | tan(x) \ \ pi / \ \2/// \ \ pi / \ \2///
| ------------------- dx = C + 2* | ------------------- dx + --------------------------------------------------- + ----------------------------------------------------
| 2 2 | 2 2 2 2
| sin (x) + 2*cos (x) | sin (x) + 2*cos (x)
| |
/ /
$$\int \frac{2 \tan{\left(x \right)} + 3}{\sin^{2}{\left(x \right)} + 2 \cos^{2}{\left(x \right)}}\, dx = C + \frac{3 \sqrt{2} \left(\operatorname{atan}{\left(\sqrt{2} \tan{\left(\frac{x}{2} \right)} - 1 \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{2} + \frac{3 \sqrt{2} \left(\operatorname{atan}{\left(\sqrt{2} \tan{\left(\frac{x}{2} \right)} + 1 \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{2} + 2 \int \frac{\tan{\left(x \right)}}{\sin^{2}{\left(x \right)} + 2 \cos^{2}{\left(x \right)}}\, dx$$
Respuesta
[src]
1 / | | 3 + 2*tan(x) | ------------------- dx | 2 2 | sin (x) + 2*cos (x) | / 0
$$\int\limits_{0}^{1} \frac{2 \tan{\left(x \right)} + 3}{\sin^{2}{\left(x \right)} + 2 \cos^{2}{\left(x \right)}}\, dx$$
=
=
1 / | | 3 + 2*tan(x) | ------------------- dx | 2 2 | sin (x) + 2*cos (x) | / 0
$$\int\limits_{0}^{1} \frac{2 \tan{\left(x \right)} + 3}{\sin^{2}{\left(x \right)} + 2 \cos^{2}{\left(x \right)}}\, dx$$
Integral((3 + 2*tan(x))/(sin(x)^2 + 2*cos(x)^2), (x, 0, 1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.