Sr Examen
Integral de 1/(sin^2(x)cos^3(x)) dx
Solución
Ha introducido
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oo / | | 1 | --------------- dx | 2 3 | sin (x)*cos (x) | / 2
$$\int\limits_{2}^{\infty} \frac{1}{\sin^{2}{\left(x \right)} \cos^{3}{\left(x \right)}}\, dx$$
Integral(1/(sin(x)^2*cos(x)^3), (x, 2, oo))
Respuesta (Indefinida)
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/ | 2 | 1 3*log(-1 + sin(x)) 3*log(1 + sin(x)) -2 + 3*sin (x) | --------------- dx = C - ------------------ + ----------------- - --------------------- | 2 3 4 4 3 | sin (x)*cos (x) -2*sin(x) + 2*sin (x) | /
$$\int \frac{1}{\sin^{2}{\left(x \right)} \cos^{3}{\left(x \right)}}\, dx = C - \frac{3 \sin^{2}{\left(x \right)} - 2}{2 \sin^{3}{\left(x \right)} - 2 \sin{\left(x \right)}} - \frac{3 \log{\left(\sin{\left(x \right)} - 1 \right)}}{4} + \frac{3 \log{\left(\sin{\left(x \right)} + 1 \right)}}{4}$$
Respuesta
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oo / | | 1 | --------------- dx | 3 2 | cos (x)*sin (x) | / 2
$$\int\limits_{2}^{\infty} \frac{1}{\sin^{2}{\left(x \right)} \cos^{3}{\left(x \right)}}\, dx$$
=
=
oo / | | 1 | --------------- dx | 3 2 | cos (x)*sin (x) | / 2
$$\int\limits_{2}^{\infty} \frac{1}{\sin^{2}{\left(x \right)} \cos^{3}{\left(x \right)}}\, dx$$
Integral(1/(cos(x)^3*sin(x)^2), (x, 2, oo))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.