Sr Examen
Integral de (6+tg(x))/(9sin²x+4cos²x) dx
Solución
Ha introducido
[src]
atan(2/3)
/
|
| 6 + tan(x)
| --------------------- dx
| 2 2
| 9*sin (x) + 4*cos (x)
|
/
0
$$\int\limits_{0}^{\operatorname{atan}{\left(\frac{2}{3} \right)}} \frac{\tan{\left(x \right)} + 6}{9 \sin^{2}{\left(x \right)} + 4 \cos^{2}{\left(x \right)}}\, dx$$
Integral((6 + tan(x))/(9*sin(x)^2 + 4*cos(x)^2), (x, 0, atan(2/3)))
Respuesta (Indefinida)
[src]
/ /x pi\ / ___ /x\ \\ / /x pi\ / ___ /x\ \\ / /x pi\ / ___ /x\ \\ / /x pi\ / ___ /x\ \\
| |- - --| | \/ 2 *tan|-| || | |- - --| | \/ 2 *tan|-| || _____________ _____________ | |- - --| | \/ 2 *tan|-| || _____________ _____________ | |- - --| | \/ 2 *tan|-| ||
____ | |2 2 | | \2/ || ___ | |2 2 | | \2/ || ____ / ___ / ___ | |2 2 | | \2/ || ___ / ___ / ___ | |2 2 | | \2/ ||
36*\/ 10 *|pi*floor|------| + atan|----------------|| 84*\/ 2 *|pi*floor|------| + atan|----------------|| 18*\/ 10 *\/ 7 - 3*\/ 5 *\/ 7 + 3*\/ 5 *|pi*floor|------| + atan|----------------|| 42*\/ 2 *\/ 7 - 3*\/ 5 *\/ 7 + 3*\/ 5 *|pi*floor|------| + atan|----------------||
/ | \ pi / | _____________|| | \ pi / | _____________|| | \ pi / | _____________|| | \ pi / | _____________|| /
| | | / ___ || | | / ___ || | | / ___ || | | / ___ || |
| 6 + tan(x) \ \\/ 7 - 3*\/ 5 // \ \\/ 7 - 3*\/ 5 // \ \\/ 7 + 3*\/ 5 // \ \\/ 7 + 3*\/ 5 // | tan(x)
| --------------------- dx = C + ----------------------------------------------------- + ---------------------------------------------------- + --------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------- + | --------------------- dx
| 2 2 _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ | 2 2
| 9*sin (x) + 4*cos (x) / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ | 4*cos (x) + 9*sin (x)
| 216*\/ 7 - 3*\/ 5 + 96*\/ 5 *\/ 7 - 3*\/ 5 216*\/ 7 - 3*\/ 5 + 96*\/ 5 *\/ 7 - 3*\/ 5 216*\/ 7 - 3*\/ 5 + 96*\/ 5 *\/ 7 - 3*\/ 5 216*\/ 7 - 3*\/ 5 + 96*\/ 5 *\/ 7 - 3*\/ 5 |
/ /
$$\int \frac{\tan{\left(x \right)} + 6}{9 \sin^{2}{\left(x \right)} + 4 \cos^{2}{\left(x \right)}}\, dx = C + \frac{36 \sqrt{10} \left(\operatorname{atan}{\left(\frac{\sqrt{2} \tan{\left(\frac{x}{2} \right)}}{\sqrt{7 - 3 \sqrt{5}}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{96 \sqrt{5} \sqrt{7 - 3 \sqrt{5}} + 216 \sqrt{7 - 3 \sqrt{5}}} + \frac{84 \sqrt{2} \left(\operatorname{atan}{\left(\frac{\sqrt{2} \tan{\left(\frac{x}{2} \right)}}{\sqrt{7 - 3 \sqrt{5}}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{96 \sqrt{5} \sqrt{7 - 3 \sqrt{5}} + 216 \sqrt{7 - 3 \sqrt{5}}} + \frac{18 \sqrt{10} \sqrt{7 - 3 \sqrt{5}} \sqrt{3 \sqrt{5} + 7} \left(\operatorname{atan}{\left(\frac{\sqrt{2} \tan{\left(\frac{x}{2} \right)}}{\sqrt{3 \sqrt{5} + 7}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{96 \sqrt{5} \sqrt{7 - 3 \sqrt{5}} + 216 \sqrt{7 - 3 \sqrt{5}}} + \frac{42 \sqrt{2} \sqrt{7 - 3 \sqrt{5}} \sqrt{3 \sqrt{5} + 7} \left(\operatorname{atan}{\left(\frac{\sqrt{2} \tan{\left(\frac{x}{2} \right)}}{\sqrt{3 \sqrt{5} + 7}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{96 \sqrt{5} \sqrt{7 - 3 \sqrt{5}} + 216 \sqrt{7 - 3 \sqrt{5}}} + \int \frac{\tan{\left(x \right)}}{9 \sin^{2}{\left(x \right)} + 4 \cos^{2}{\left(x \right)}}\, dx$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.