Sr Examen
Integral de 1/(sinx+2) dx
Solución
Ha introducido
[src]
2*x / | | 1 | ---------- dx | sin(x) + 2 | / 0
$$\int\limits_{0}^{2 x} \frac{1}{\sin{\left(x \right)} + 2}\, dx$$
Integral(1/(sin(x) + 2), (x, 0, 2*x))
Respuesta (Indefinida)
[src]
/ /x pi\ / ___ /x\\\
| |- - --| | ___ 2*\/ 3 *tan|-|||
/ ___ | |2 2 | |\/ 3 \2/||
| 2*\/ 3 *|pi*floor|------| + atan|----- + --------------||
| 1 \ \ pi / \ 3 3 //
| ---------- dx = C + ---------------------------------------------------------
| sin(x) + 2 3
|
/
$$\int \frac{1}{\sin{\left(x \right)} + 2}\, dx = C + \frac{2 \sqrt{3} \left(\operatorname{atan}{\left(\frac{2 \sqrt{3} \tan{\left(\frac{x}{2} \right)}}{3} + \frac{\sqrt{3}}{3} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{3}$$
Respuesta
[src]
/ / pi\ \
| |x - --| / ___ ___ \|
___ | | 2 | |\/ 3 2*\/ 3 *tan(x)||
2*\/ 3 *|pi*floor|------| + atan|----- + --------------|| ___
\ \ pi / \ 3 3 // 5*pi*\/ 3
--------------------------------------------------------- + ----------
3 9
$$\frac{2 \sqrt{3} \left(\operatorname{atan}{\left(\frac{2 \sqrt{3} \tan{\left(x \right)}}{3} + \frac{\sqrt{3}}{3} \right)} + \pi \left\lfloor{\frac{x - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{3} + \frac{5 \sqrt{3} \pi}{9}$$
=
=
/ / pi\ \
| |x - --| / ___ ___ \|
___ | | 2 | |\/ 3 2*\/ 3 *tan(x)||
2*\/ 3 *|pi*floor|------| + atan|----- + --------------|| ___
\ \ pi / \ 3 3 // 5*pi*\/ 3
--------------------------------------------------------- + ----------
3 9
$$\frac{2 \sqrt{3} \left(\operatorname{atan}{\left(\frac{2 \sqrt{3} \tan{\left(x \right)}}{3} + \frac{\sqrt{3}}{3} \right)} + \pi \left\lfloor{\frac{x - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{3} + \frac{5 \sqrt{3} \pi}{9}$$
2*sqrt(3)*(pi*floor((x - pi/2)/pi) + atan(sqrt(3)/3 + 2*sqrt(3)*tan(x)/3))/3 + 5*pi*sqrt(3)/9
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.