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