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