Sr Examen
Integral de 1/(sin(6x)+7) dx
Solución
Ha introducido
[src]
1 / | | 1 | ------------ dx | sin(6*x) + 7 | / 0
$$\int\limits_{0}^{1} \frac{1}{\sin{\left(6 x \right)} + 7}\, dx$$
Integral(1/(sin(6*x) + 7), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / pi\ \
| |3*x - --| / ___ ___ \|
/ ___ | | 2 | |\/ 3 7*\/ 3 *tan(3*x)||
| \/ 3 *|pi*floor|--------| + atan|----- + ----------------||
| 1 \ \ pi / \ 12 12 //
| ------------ dx = C + -----------------------------------------------------------
| sin(6*x) + 7 36
|
/
$$\int \frac{1}{\sin{\left(6 x \right)} + 7}\, dx = C + \frac{\sqrt{3} \left(\operatorname{atan}{\left(\frac{7 \sqrt{3} \tan{\left(3 x \right)}}{12} + \frac{\sqrt{3}}{12} \right)} + \pi \left\lfloor{\frac{3 x - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{36}$$
Gráfica
Respuesta
[src]
/ / ___\\ / ___ ___ \
___ | |\/ 3 || ___ |\/ 3 7*\/ 3 *tan(3)|
\/ 3 *|-pi + atan|-----|| \/ 3 *atan|----- + --------------|
\ \ 12 // \ 12 12 /
- ------------------------- + ----------------------------------
36 36
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{7 \sqrt{3} \tan{\left(3 \right)}}{12} + \frac{\sqrt{3}}{12} \right)}}{36} - \frac{\sqrt{3} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{3}}{12} \right)}\right)}{36}$$
=
=
/ / ___\\ / ___ ___ \
___ | |\/ 3 || ___ |\/ 3 7*\/ 3 *tan(3)|
\/ 3 *|-pi + atan|-----|| \/ 3 *atan|----- + --------------|
\ \ 12 // \ 12 12 /
- ------------------------- + ----------------------------------
36 36
$$\frac{\sqrt{3} \operatorname{atan}{\left(\frac{7 \sqrt{3} \tan{\left(3 \right)}}{12} + \frac{\sqrt{3}}{12} \right)}}{36} - \frac{\sqrt{3} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{3}}{12} \right)}\right)}{36}$$
-sqrt(3)*(-pi + atan(sqrt(3)/12))/36 + sqrt(3)*atan(sqrt(3)/12 + 7*sqrt(3)*tan(3)/12)/36
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.