Sr Examen
Integral de 1/(sin^2(5x-1)) dx
Solución
Ha introducido
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1 / | | 1 | ------------- dx | 2 | sin (5*x - 1) | / 0
$$\int\limits_{0}^{1} \frac{1}{\sin^{2}{\left(5 x - 1 \right)}}\, dx$$
Integral(1/(sin(5*x - 1)^2), (x, 0, 1))
Respuesta (Indefinida)
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/ / 1 5*x\ | tan|- - + ---| | 1 1 \ 2 2 / | ------------- dx = C - ----------------- + -------------- | 2 / 1 5*x\ 10 | sin (5*x - 1) 10*tan|- - + ---| | \ 2 2 / /
$$\int \frac{1}{\sin^{2}{\left(5 x - 1 \right)}}\, dx = C + \frac{\tan{\left(\frac{5 x}{2} - \frac{1}{2} \right)}}{10} - \frac{1}{10 \tan{\left(\frac{5 x}{2} - \frac{1}{2} \right)}}$$
Gráfica
Respuesta
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1 1 tan(1/2) tan(2) - ----------- - --------- + -------- + ------ 10*tan(1/2) 10*tan(2) 10 10
$$\frac{\tan{\left(2 \right)}}{10} - \frac{1}{10 \tan{\left(\frac{1}{2} \right)}} - \frac{1}{10 \tan{\left(2 \right)}} + \frac{\tan{\left(\frac{1}{2} \right)}}{10}$$
=
=
1 1 tan(1/2) tan(2) - ----------- - --------- + -------- + ------ 10*tan(1/2) 10*tan(2) 10 10
$$\frac{\tan{\left(2 \right)}}{10} - \frac{1}{10 \tan{\left(\frac{1}{2} \right)}} - \frac{1}{10 \tan{\left(2 \right)}} + \frac{\tan{\left(\frac{1}{2} \right)}}{10}$$
-1/(10*tan(1/2)) - 1/(10*tan(2)) + tan(1/2)/10 + tan(2)/10
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.