Sr Examen
Integral de 1/(2sin(x)^2-cos(x)^2) dx
Solución
Ha introducido
[src]
1 / | | 1 | ------------------- dx | 2 2 | 2*sin (x) - cos (x) | / 0
$$\int\limits_{0}^{1} \frac{1}{2 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}}\, dx$$
Integral(1/(2*sin(x)^2 - cos(x)^2), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ _____________ \ / _____________ \ / _____________ \ / _____________ \ _____________ _____________ / _____________ \ _____________ _____________ / _____________ \ _____________ _____________ / _____________ \ _____________ _____________ / _____________ \ / | / ___ /x\| | / ___ /x\| ___ | / ___ /x\| ___ | / ___ /x\| / ___ / ___ | / ___ /x\| / ___ / ___ | / ___ /x\| ___ / ___ / ___ | / ___ /x\| ___ / ___ / ___ | / ___ /x\| | 267*log|\/ 5 - 2*\/ 6 + tan|-|| 267*log|- \/ 5 - 2*\/ 6 + tan|-|| 109*\/ 6 *log|\/ 5 - 2*\/ 6 + tan|-|| 109*\/ 6 *log|- \/ 5 - 2*\/ 6 + tan|-|| 267*\/ 5 - 2*\/ 6 *\/ 5 + 2*\/ 6 *log|- \/ 5 + 2*\/ 6 + tan|-|| 267*\/ 5 - 2*\/ 6 *\/ 5 + 2*\/ 6 *log|\/ 5 + 2*\/ 6 + tan|-|| 109*\/ 6 *\/ 5 - 2*\/ 6 *\/ 5 + 2*\/ 6 *log|- \/ 5 + 2*\/ 6 + tan|-|| 109*\/ 6 *\/ 5 - 2*\/ 6 *\/ 5 + 2*\/ 6 *log|\/ 5 + 2*\/ 6 + tan|-|| | 1 \ \2// \ \2// \ \2// \ \2// \ \2// \ \2// \ \2// \ \2// | ------------------- dx = C - -------------------------------------------------- + -------------------------------------------------- - -------------------------------------------------- + -------------------------------------------------- - ---------------------------------------------------------------------- + -------------------------------------------------------------------- - ---------------------------------------------------------------------------- + -------------------------------------------------------------------------- | 2 2 _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ _____________ | 2*sin (x) - cos (x) / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ / ___ ___ / ___ | 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 2376*\/ 5 - 2*\/ 6 + 970*\/ 6 *\/ 5 - 2*\/ 6 /
$$\int \frac{1}{2 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}}\, dx = C + \frac{109 \sqrt{6} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{5 - 2 \sqrt{6}} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} + \frac{267 \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{5 - 2 \sqrt{6}} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} - \frac{267 \log{\left(\tan{\left(\frac{x}{2} \right)} + \sqrt{5 - 2 \sqrt{6}} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} - \frac{109 \sqrt{6} \log{\left(\tan{\left(\frac{x}{2} \right)} + \sqrt{5 - 2 \sqrt{6}} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} - \frac{267 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2 \sqrt{6} + 5} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} - \frac{109 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{x}{2} \right)} - \sqrt{2 \sqrt{6} + 5} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} + \frac{109 \sqrt{6} \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{x}{2} \right)} + \sqrt{2 \sqrt{6} + 5} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}} + \frac{267 \sqrt{5 - 2 \sqrt{6}} \sqrt{2 \sqrt{6} + 5} \log{\left(\tan{\left(\frac{x}{2} \right)} + \sqrt{2 \sqrt{6} + 5} \right)}}{2376 \sqrt{5 - 2 \sqrt{6}} + 970 \sqrt{6} \sqrt{5 - 2 \sqrt{6}}}$$
Gráfica
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.