Sr Examen
Integral de (3*tg(x)+1)/(2*sin(2x)-5*cos(2x)+1) dx
Solución
Ha introducido
[src]
0
/
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| 3*tan(x) + 1
| --------------------------- dx
| 2*sin(2*x) - 5*cos(2*x) + 1
|
/
-atan(1/3)
$$\int\limits_{- \operatorname{atan}{\left(\frac{1}{3} \right)}}^{0} \frac{3 \tan{\left(x \right)} + 1}{\left(2 \sin{\left(2 x \right)} - 5 \cos{\left(2 x \right)}\right) + 1}\, dx$$
Integral((3*tan(x) + 1)/(2*sin(2*x) - 5*cos(2*x) + 1), (x, -atan(1/3), 0))
Respuesta (Indefinida)
[src]
/ ___ \ / ___ \ / / ___ |1 \/ 7 | ___ |1 \/ 7 | | | \/ 7 *log|- + ----- + tan(x)| \/ 7 *log|- - ----- + tan(x)| | 3*tan(x) + 1 | tan(x) \3 3 / \3 3 / | --------------------------- dx = C - 3* | ---------------------------- dx - ----------------------------- + ----------------------------- | 2*sin(2*x) - 5*cos(2*x) + 1 | -1 - 2*sin(2*x) + 5*cos(2*x) 28 28 | | / /
$$\int \frac{3 \tan{\left(x \right)} + 1}{\left(2 \sin{\left(2 x \right)} - 5 \cos{\left(2 x \right)}\right) + 1}\, dx = C - \frac{\sqrt{7} \log{\left(\tan{\left(x \right)} + \frac{1}{3} + \frac{\sqrt{7}}{3} \right)}}{28} + \frac{\sqrt{7} \log{\left(\tan{\left(x \right)} - \frac{\sqrt{7}}{3} + \frac{1}{3} \right)}}{28} - 3 \int \frac{\tan{\left(x \right)}}{- 2 \sin{\left(2 x \right)} + 5 \cos{\left(2 x \right)} - 1}\, dx$$
Respuesta
[src]
0 0
/ /
| |
| 1 | 3*tan(x)
- | ---------------------------- dx - | ---------------------------- dx
| -1 - 2*sin(2*x) + 5*cos(2*x) | -1 - 2*sin(2*x) + 5*cos(2*x)
| |
/ /
-atan(1/3) -atan(1/3)
$$- \int\limits_{- \operatorname{atan}{\left(\frac{1}{3} \right)}}^{0} \frac{1}{- 2 \sin{\left(2 x \right)} + 5 \cos{\left(2 x \right)} - 1}\, dx - \int\limits_{- \operatorname{atan}{\left(\frac{1}{3} \right)}}^{0} \frac{3 \tan{\left(x \right)}}{- 2 \sin{\left(2 x \right)} + 5 \cos{\left(2 x \right)} - 1}\, dx$$
=
=
0 0
/ /
| |
| 1 | 3*tan(x)
- | ---------------------------- dx - | ---------------------------- dx
| -1 - 2*sin(2*x) + 5*cos(2*x) | -1 - 2*sin(2*x) + 5*cos(2*x)
| |
/ /
-atan(1/3) -atan(1/3)
$$- \int\limits_{- \operatorname{atan}{\left(\frac{1}{3} \right)}}^{0} \frac{1}{- 2 \sin{\left(2 x \right)} + 5 \cos{\left(2 x \right)} - 1}\, dx - \int\limits_{- \operatorname{atan}{\left(\frac{1}{3} \right)}}^{0} \frac{3 \tan{\left(x \right)}}{- 2 \sin{\left(2 x \right)} + 5 \cos{\left(2 x \right)} - 1}\, dx$$
-Integral(1/(-1 - 2*sin(2*x) + 5*cos(2*x)), (x, -atan(1/3), 0)) - Integral(3*tan(x)/(-1 - 2*sin(2*x) + 5*cos(2*x)), (x, -atan(1/3), 0))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.