Sr Examen
Integral de dx/sin^2(3x-1) dx
Solución
Ha introducido
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1 / | | 1 | ------------- dx | 2 | sin (3*x - 1) | / 0
$$\int\limits_{0}^{1} \frac{1}{\sin^{2}{\left(3 x - 1 \right)}}\, dx$$
Integral(1/(sin(3*x - 1)^2), (x, 0, 1))
Respuesta (Indefinida)
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/ / 1 3*x\ | tan|- - + ---| | 1 1 \ 2 2 / | ------------- dx = C - ---------------- + -------------- | 2 / 1 3*x\ 6 | sin (3*x - 1) 6*tan|- - + ---| | \ 2 2 / /
$$\int \frac{1}{\sin^{2}{\left(3 x - 1 \right)}}\, dx = C + \frac{\tan{\left(\frac{3 x}{2} - \frac{1}{2} \right)}}{6} - \frac{1}{6 \tan{\left(\frac{3 x}{2} - \frac{1}{2} \right)}}$$
Gráfica
Respuesta
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1 1 tan(1) tan(1/2) - -------- - ---------- + ------ + -------- 6*tan(1) 6*tan(1/2) 6 6
$$- \frac{1}{6 \tan{\left(\frac{1}{2} \right)}} - \frac{1}{6 \tan{\left(1 \right)}} + \frac{\tan{\left(\frac{1}{2} \right)}}{6} + \frac{\tan{\left(1 \right)}}{6}$$
=
=
1 1 tan(1) tan(1/2) - -------- - ---------- + ------ + -------- 6*tan(1) 6*tan(1/2) 6 6
$$- \frac{1}{6 \tan{\left(\frac{1}{2} \right)}} - \frac{1}{6 \tan{\left(1 \right)}} + \frac{\tan{\left(\frac{1}{2} \right)}}{6} + \frac{\tan{\left(1 \right)}}{6}$$
-1/(6*tan(1)) - 1/(6*tan(1/2)) + tan(1)/6 + tan(1/2)/6
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.