Sr Examen
Integral de 1/(sin^5x*cos^5x) dx
Solución
Ha introducido
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1 / | | 1 | --------------- dx | 5 5 | sin (x)*cos (x) | / 0
$$\int\limits_{0}^{1} \frac{1}{\sin^{5}{\left(x \right)} \cos^{5}{\left(x \right)}}\, dx$$
Integral(1/(sin(x)^5*cos(x)^5), (x, 0, 1))
Respuesta (Indefinida)
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/ | 4 2 6 | 1 / 2 \ 1 - 18*sin (x) + 4*sin (x) + 12*sin (x) | --------------- dx = C - 3*log\-1 + sin (x)/ + 6*log(sin(x)) - --------------------------------------- | 5 5 6 4 8 | sin (x)*cos (x) - 8*sin (x) + 4*sin (x) + 4*sin (x) | /
$$\int \frac{1}{\sin^{5}{\left(x \right)} \cos^{5}{\left(x \right)}}\, dx = C - 3 \log{\left(\sin^{2}{\left(x \right)} - 1 \right)} + 6 \log{\left(\sin{\left(x \right)} \right)} - \frac{12 \sin^{6}{\left(x \right)} - 18 \sin^{4}{\left(x \right)} + 4 \sin^{2}{\left(x \right)} + 1}{4 \sin^{8}{\left(x \right)} - 8 \sin^{6}{\left(x \right)} + 4 \sin^{4}{\left(x \right)}}$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.