Sr Examen
Integral de (2sinx)/(-sin^2x+cosx+2) dx
Solución
Ha introducido
[src]
1 / | | 2*sin(x) | ---------------------- dx | 2 | - sin (x) + cos(x) + 2 | / 0
$$\int\limits_{0}^{1} \frac{2 \sin{\left(x \right)}}{\left(- \sin^{2}{\left(x \right)} + \cos{\left(x \right)}\right) + 2}\, dx$$
Integral((2*sin(x))/(-sin(x)^2 + cos(x) + 2), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ /x pi\ / ___ 3/4 /x\\\ / /x pi\ / ___ 3/4 /x\\\
| |- - --| | \/ 2 *3 *tan|-||| | |- - --| | \/ 2 *3 *tan|-|||
/ ___ | |2 2 | | \2/|| ___ | |2 2 | | \2/||
| 4*\/ 3 *|pi*floor|------| + atan|1 + -----------------|| 4*\/ 3 *|pi*floor|------| + atan|-1 + -----------------||
| 2*sin(x) \ \ pi / \ 3 // \ \ pi / \ 3 //
| ---------------------- dx = C - -------------------------------------------------------- + ---------------------------------------------------------
| 2 3 3
| - sin (x) + cos(x) + 2
|
/
$$\int \frac{2 \sin{\left(x \right)}}{\left(- \sin^{2}{\left(x \right)} + \cos{\left(x \right)}\right) + 2}\, dx = C + \frac{4 \sqrt{3} \left(\operatorname{atan}{\left(\frac{\sqrt{2} \cdot 3^{\frac{3}{4}} \tan{\left(\frac{x}{2} \right)}}{3} - 1 \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{3} - \frac{4 \sqrt{3} \left(\operatorname{atan}{\left(\frac{\sqrt{2} \cdot 3^{\frac{3}{4}} \tan{\left(\frac{x}{2} \right)}}{3} + 1 \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{3}$$
Respuesta
[src]
1
/
|
| sin(x)
2* | -------------------- dx
| 2
| 2 - sin (x) + cos(x)
|
/
0
$$2 \int\limits_{0}^{1} \frac{\sin{\left(x \right)}}{- \sin^{2}{\left(x \right)} + \cos{\left(x \right)} + 2}\, dx$$
=
=
1
/
|
| sin(x)
2* | -------------------- dx
| 2
| 2 - sin (x) + cos(x)
|
/
0
$$2 \int\limits_{0}^{1} \frac{\sin{\left(x \right)}}{- \sin^{2}{\left(x \right)} + \cos{\left(x \right)} + 2}\, dx$$
2*Integral(sin(x)/(2 - sin(x)^2 + cos(x)), (x, 0, 1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.