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