Sr Examen
Integral de 1/(5sinx^2-3cosx^2) dx
Solución
Ha introducido
[src]
1 / | | 1 | --------------------- dx | 2 2 | 5*sin (x) - 3*cos (x) | / 0
$$\int\limits_{0}^{1} \frac{1}{5 \sin^{2}{\left(x \right)} - 3 \cos^{2}{\left(x \right)}}\, dx$$
Integral(1/(5*sin(x)^2 - 3*cos(x)^2), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ _______________ \ / _______________ \ / _______________ \ / _______________ \ / _______________ \ / _______________ \ / _______________ \ / _______________ \
| ___ / ____ | | ___ / ____ | | ___ / ____ | | ___ / ____ | _______________ _______________ | ___ / ____ | _______________ _______________ | ___ / ____ | _______________ _______________ | ___ / ____ | _______________ _______________ | ___ / ____ |
/ ___ |\/ 3 *\/ 13 - 4*\/ 10 /x\| ____ |\/ 3 *\/ 13 - 4*\/ 10 /x\| ____ | \/ 3 *\/ 13 - 4*\/ 10 /x\| ___ | \/ 3 *\/ 13 - 4*\/ 10 /x\| ___ / ____ / ____ | \/ 3 *\/ 13 + 4*\/ 10 /x\| ____ / ____ / ____ | \/ 3 *\/ 13 + 4*\/ 10 /x\| ____ / ____ / ____ |\/ 3 *\/ 13 + 4*\/ 10 /x\| ___ / ____ / ____ |\/ 3 *\/ 13 + 4*\/ 10 /x\|
| 7068*\/ 3 *log|------------------------ + tan|-|| 2235*\/ 30 *log|------------------------ + tan|-|| 2235*\/ 30 *log|- ------------------------ + tan|-|| 7068*\/ 3 *log|- ------------------------ + tan|-|| 2356*\/ 3 *\/ 13 - 4*\/ 10 *\/ 13 + 4*\/ 10 *log|- ------------------------ + tan|-|| 745*\/ 30 *\/ 13 - 4*\/ 10 *\/ 13 + 4*\/ 10 *log|- ------------------------ + tan|-|| 745*\/ 30 *\/ 13 - 4*\/ 10 *\/ 13 + 4*\/ 10 *log|------------------------ + tan|-|| 2356*\/ 3 *\/ 13 - 4*\/ 10 *\/ 13 + 4*\/ 10 *log|------------------------ + tan|-||
| 1 \ 3 \2// \ 3 \2// \ 3 \2// \ 3 \2// \ 3 \2// \ 3 \2// \ 3 \2// \ 3 \2//
| --------------------- dx = C - ----------------------------------------------------------- - ----------------------------------------------------------- + ----------------------------------------------------------- + ----------------------------------------------------------- - ----------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------
| 2 2 _______________ _______________ _______________ _______________ _______________ _______________ _______________ _______________ _______________ _______________ _______________ _______________ _______________ _______________ _______________ _______________
| 5*sin (x) - 3*cos (x) / ____ ____ / ____ / ____ ____ / ____ / ____ ____ / ____ / ____ ____ / ____ / ____ ____ / ____ / ____ ____ / ____ / ____ ____ / ____ / ____ ____ / ____
| 160080*\/ 13 - 4*\/ 10 + 50622*\/ 10 *\/ 13 - 4*\/ 10 160080*\/ 13 - 4*\/ 10 + 50622*\/ 10 *\/ 13 - 4*\/ 10 160080*\/ 13 - 4*\/ 10 + 50622*\/ 10 *\/ 13 - 4*\/ 10 160080*\/ 13 - 4*\/ 10 + 50622*\/ 10 *\/ 13 - 4*\/ 10 160080*\/ 13 - 4*\/ 10 + 50622*\/ 10 *\/ 13 - 4*\/ 10 160080*\/ 13 - 4*\/ 10 + 50622*\/ 10 *\/ 13 - 4*\/ 10 160080*\/ 13 - 4*\/ 10 + 50622*\/ 10 *\/ 13 - 4*\/ 10 160080*\/ 13 - 4*\/ 10 + 50622*\/ 10 *\/ 13 - 4*\/ 10
/
$$\int \frac{1}{5 \sin^{2}{\left(x \right)} - 3 \cos^{2}{\left(x \right)}}\, dx = C + \frac{2235 \sqrt{30} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{3} \sqrt{13 - 4 \sqrt{10}}}{3} \right)}}{160080 \sqrt{13 - 4 \sqrt{10}} + 50622 \sqrt{10} \sqrt{13 - 4 \sqrt{10}}} + \frac{7068 \sqrt{3} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{3} \sqrt{13 - 4 \sqrt{10}}}{3} \right)}}{160080 \sqrt{13 - 4 \sqrt{10}} + 50622 \sqrt{10} \sqrt{13 - 4 \sqrt{10}}} - \frac{7068 \sqrt{3} \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{\sqrt{3} \sqrt{13 - 4 \sqrt{10}}}{3} \right)}}{160080 \sqrt{13 - 4 \sqrt{10}} + 50622 \sqrt{10} \sqrt{13 - 4 \sqrt{10}}} - \frac{2235 \sqrt{30} \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{\sqrt{3} \sqrt{13 - 4 \sqrt{10}}}{3} \right)}}{160080 \sqrt{13 - 4 \sqrt{10}} + 50622 \sqrt{10} \sqrt{13 - 4 \sqrt{10}}} - \frac{2356 \sqrt{3} \sqrt{13 - 4 \sqrt{10}} \sqrt{4 \sqrt{10} + 13} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{3} \sqrt{4 \sqrt{10} + 13}}{3} \right)}}{160080 \sqrt{13 - 4 \sqrt{10}} + 50622 \sqrt{10} \sqrt{13 - 4 \sqrt{10}}} - \frac{745 \sqrt{30} \sqrt{13 - 4 \sqrt{10}} \sqrt{4 \sqrt{10} + 13} \log{\left(\tan{\left(\frac{x}{2} \right)} - \frac{\sqrt{3} \sqrt{4 \sqrt{10} + 13}}{3} \right)}}{160080 \sqrt{13 - 4 \sqrt{10}} + 50622 \sqrt{10} \sqrt{13 - 4 \sqrt{10}}} + \frac{745 \sqrt{30} \sqrt{13 - 4 \sqrt{10}} \sqrt{4 \sqrt{10} + 13} \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{\sqrt{3} \sqrt{4 \sqrt{10} + 13}}{3} \right)}}{160080 \sqrt{13 - 4 \sqrt{10}} + 50622 \sqrt{10} \sqrt{13 - 4 \sqrt{10}}} + \frac{2356 \sqrt{3} \sqrt{13 - 4 \sqrt{10}} \sqrt{4 \sqrt{10} + 13} \log{\left(\tan{\left(\frac{x}{2} \right)} + \frac{\sqrt{3} \sqrt{4 \sqrt{10} + 13}}{3} \right)}}{160080 \sqrt{13 - 4 \sqrt{10}} + 50622 \sqrt{10} \sqrt{13 - 4 \sqrt{10}}}$$
Gráfica
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.