Sr Examen
Integral de (3*tgx-10)/((tgx-5)*sin2x) dx
Solución
Ha introducido
[src]
atan(2)
/
|
| 3*tan(x) - 10
| --------------------- dx
| (tan(x) - 5)*sin(2*x)
|
/
pi
--
4
$$\int\limits_{\frac{\pi}{4}}^{\operatorname{atan}{\left(2 \right)}} \frac{3 \tan{\left(x \right)} - 10}{\left(\tan{\left(x \right)} - 5\right) \sin{\left(2 x \right)}}\, dx$$
Integral((3*tan(x) - 10)/(((tan(x) - 5)*sin(2*x))), (x, pi/4, atan(2)))
Respuesta (Indefinida)
[src]
/ / / | | | | 3*tan(x) - 10 | 1 | tan(x) | --------------------- dx = C - 10* | ---------------------- dx + 3* | ---------------------- dx | (tan(x) - 5)*sin(2*x) | (-5 + tan(x))*sin(2*x) | (-5 + tan(x))*sin(2*x) | | | / / /
$$\int \frac{3 \tan{\left(x \right)} - 10}{\left(\tan{\left(x \right)} - 5\right) \sin{\left(2 x \right)}}\, dx = C - 10 \int \frac{1}{\left(\tan{\left(x \right)} - 5\right) \sin{\left(2 x \right)}}\, dx + 3 \int \frac{\tan{\left(x \right)}}{\left(\tan{\left(x \right)} - 5\right) \sin{\left(2 x \right)}}\, dx$$
Respuesta
[src]
atan(2)
/
|
| -10 + 3*tan(x)
| ---------------------- dx
| (-5 + tan(x))*sin(2*x)
|
/
pi
--
4
$$\int\limits_{\frac{\pi}{4}}^{\operatorname{atan}{\left(2 \right)}} \frac{3 \tan{\left(x \right)} - 10}{\left(\tan{\left(x \right)} - 5\right) \sin{\left(2 x \right)}}\, dx$$
=
=
atan(2)
/
|
| -10 + 3*tan(x)
| ---------------------- dx
| (-5 + tan(x))*sin(2*x)
|
/
pi
--
4
$$\int\limits_{\frac{\pi}{4}}^{\operatorname{atan}{\left(2 \right)}} \frac{3 \tan{\left(x \right)} - 10}{\left(\tan{\left(x \right)} - 5\right) \sin{\left(2 x \right)}}\, dx$$
Integral((-10 + 3*tan(x))/((-5 + tan(x))*sin(2*x)), (x, pi/4, atan(2)))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.