Sr Examen
Integral de 1/(3+sin5x) dx
Solución
Ha introducido
[src]
1 / | | 1 | ------------ dx | 3 + sin(5*x) | / 0
$$\int\limits_{0}^{1} \frac{1}{\sin{\left(5 x \right)} + 3}\, dx$$
Integral(1/(3 + sin(5*x)), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / pi 5*x\ / ___ /5*x\\\
| |- -- + ---| | ___ 3*\/ 2 *tan|---|||
/ ___ | | 2 2 | |\/ 2 \ 2 /||
| \/ 2 *|pi*floor|----------| + atan|----- + ----------------||
| 1 \ \ pi / \ 4 4 //
| ------------ dx = C + -------------------------------------------------------------
| 3 + sin(5*x) 10
|
/
$$\int \frac{1}{\sin{\left(5 x \right)} + 3}\, dx = C + \frac{\sqrt{2} \left(\operatorname{atan}{\left(\frac{3 \sqrt{2} \tan{\left(\frac{5 x}{2} \right)}}{4} + \frac{\sqrt{2}}{4} \right)} + \pi \left\lfloor{\frac{\frac{5 x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{10}$$
Gráfica
Respuesta
[src]
/ / ___\\ / ___ ___ \
___ | |\/ 2 || ___ |\/ 2 3*\/ 2 *tan(5/2)|
\/ 2 *|-pi + atan|-----|| \/ 2 *atan|----- + ----------------|
\ \ 4 // \ 4 4 /
- ------------------------- + ------------------------------------
10 10
$$\frac{\sqrt{2} \operatorname{atan}{\left(\frac{3 \sqrt{2} \tan{\left(\frac{5}{2} \right)}}{4} + \frac{\sqrt{2}}{4} \right)}}{10} - \frac{\sqrt{2} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{2}}{4} \right)}\right)}{10}$$
=
=
/ / ___\\ / ___ ___ \
___ | |\/ 2 || ___ |\/ 2 3*\/ 2 *tan(5/2)|
\/ 2 *|-pi + atan|-----|| \/ 2 *atan|----- + ----------------|
\ \ 4 // \ 4 4 /
- ------------------------- + ------------------------------------
10 10
$$\frac{\sqrt{2} \operatorname{atan}{\left(\frac{3 \sqrt{2} \tan{\left(\frac{5}{2} \right)}}{4} + \frac{\sqrt{2}}{4} \right)}}{10} - \frac{\sqrt{2} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{2}}{4} \right)}\right)}{10}$$
-sqrt(2)*(-pi + atan(sqrt(2)/4))/10 + sqrt(2)*atan(sqrt(2)/4 + 3*sqrt(2)*tan(5/2)/4)/10
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.