Sr Examen
Integral de 1/(sin(6*x)+3) dx
Solución
Ha introducido
[src]
1 / | | 1 | ------------ dx | sin(6*x) + 3 | / 0
$$\int\limits_{0}^{1} \frac{1}{\sin{\left(6 x \right)} + 3}\, dx$$
Integral(1/(sin(6*x) + 3), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / pi\ \
| |3*x - --| / ___ ___ \|
/ ___ | | 2 | |\/ 2 3*\/ 2 *tan(3*x)||
| \/ 2 *|pi*floor|--------| + atan|----- + ----------------||
| 1 \ \ pi / \ 4 4 //
| ------------ dx = C + -----------------------------------------------------------
| sin(6*x) + 3 12
|
/
$$\int \frac{1}{\sin{\left(6 x \right)} + 3}\, dx = C + \frac{\sqrt{2} \left(\operatorname{atan}{\left(\frac{3 \sqrt{2} \tan{\left(3 x \right)}}{4} + \frac{\sqrt{2}}{4} \right)} + \pi \left\lfloor{\frac{3 x - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{12}$$
Gráfica
Respuesta
[src]
/ / ___\\ / ___ ___ \
___ | |\/ 2 || ___ |\/ 2 3*\/ 2 *tan(3)|
\/ 2 *|-pi + atan|-----|| \/ 2 *atan|----- + --------------|
\ \ 4 // \ 4 4 /
- ------------------------- + ----------------------------------
12 12
$$\frac{\sqrt{2} \operatorname{atan}{\left(\frac{3 \sqrt{2} \tan{\left(3 \right)}}{4} + \frac{\sqrt{2}}{4} \right)}}{12} - \frac{\sqrt{2} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{2}}{4} \right)}\right)}{12}$$
=
=
/ / ___\\ / ___ ___ \
___ | |\/ 2 || ___ |\/ 2 3*\/ 2 *tan(3)|
\/ 2 *|-pi + atan|-----|| \/ 2 *atan|----- + --------------|
\ \ 4 // \ 4 4 /
- ------------------------- + ----------------------------------
12 12
$$\frac{\sqrt{2} \operatorname{atan}{\left(\frac{3 \sqrt{2} \tan{\left(3 \right)}}{4} + \frac{\sqrt{2}}{4} \right)}}{12} - \frac{\sqrt{2} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{2}}{4} \right)}\right)}{12}$$
-sqrt(2)*(-pi + atan(sqrt(2)/4))/12 + sqrt(2)*atan(sqrt(2)/4 + 3*sqrt(2)*tan(3)/4)/12
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.