Sr Examen
Integral de sin(x)*dx/(2+sin(x)) dx
Solución
Ha introducido
[src]
1 / | | sin(x) | ---------- dx | 2 + sin(x) | / 0
$$\int\limits_{0}^{1} \frac{\sin{\left(x \right)}}{\sin{\left(x \right)} + 2}\, dx$$
Integral(sin(x)/(2 + sin(x)), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ /x pi\ / ___ /x\\\
| |- - --| | ___ 2*\/ 3 *tan|-|||
/ ___ | |2 2 | |\/ 3 \2/||
| 4*\/ 3 *|pi*floor|------| + atan|----- + --------------||
| sin(x) \ \ pi / \ 3 3 //
| ---------- dx = C + x - ---------------------------------------------------------
| 2 + sin(x) 3
|
/
$$\int \frac{\sin{\left(x \right)}}{\sin{\left(x \right)} + 2}\, dx = C + x - \frac{4 \sqrt{3} \left(\operatorname{atan}{\left(\frac{2 \sqrt{3} \tan{\left(\frac{x}{2} \right)}}{3} + \frac{\sqrt{3}}{3} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{3}$$
Gráfica
Respuesta
[src]
/ / ___ ___ \\
___ | |\/ 3 2*\/ 3 *tan(1/2)||
___ 4*\/ 3 *|-pi + atan|----- + ----------------||
10*pi*\/ 3 \ \ 3 3 //
1 - ----------- - ----------------------------------------------
9 3
$$- \frac{10 \sqrt{3} \pi}{9} + 1 - \frac{4 \sqrt{3} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{3}}{3} + \frac{2 \sqrt{3} \tan{\left(\frac{1}{2} \right)}}{3} \right)}\right)}{3}$$
=
=
/ / ___ ___ \\
___ | |\/ 3 2*\/ 3 *tan(1/2)||
___ 4*\/ 3 *|-pi + atan|----- + ----------------||
10*pi*\/ 3 \ \ 3 3 //
1 - ----------- - ----------------------------------------------
9 3
$$- \frac{10 \sqrt{3} \pi}{9} + 1 - \frac{4 \sqrt{3} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{3}}{3} + \frac{2 \sqrt{3} \tan{\left(\frac{1}{2} \right)}}{3} \right)}\right)}{3}$$
1 - 10*pi*sqrt(3)/9 - 4*sqrt(3)*(-pi + atan(sqrt(3)/3 + 2*sqrt(3)*tan(1/2)/3))/3
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.