Sr Examen
Integral de 1/(sin^33x×cosx) dx
Solución
Ha introducido
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1 / | | 1 | --------------- dx | 33 | sin (x)*cos(x) | / 0
$$\int\limits_{0}^{1} \frac{1}{\sin^{33}{\left(x \right)} \cos{\left(x \right)}}\, dx$$
Integral(1/(sin(x)^33*cos(x)), (x, 0, 1))
Respuesta (Indefinida)
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/ | / 2 \ 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 | 1 log\-1 + sin (x)/ 45045 + 48048*sin (x) + 51480*sin (x) + 55440*sin (x) + 60060*sin (x) + 65520*sin (x) + 72072*sin (x) + 80080*sin (x) + 90090*sin (x) + 102960*sin (x) + 120120*sin (x) + 144144*sin (x) + 180180*sin (x) + 240240*sin (x) + 360360*sin (x) + 720720*sin (x) | --------------- dx = C - ----------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + log(sin(x)) | 33 2 32 | sin (x)*cos(x) 1441440*sin (x) | /
$$\int \frac{1}{\sin^{33}{\left(x \right)} \cos{\left(x \right)}}\, dx = C - \frac{720720 \sin^{30}{\left(x \right)} + 360360 \sin^{28}{\left(x \right)} + 240240 \sin^{26}{\left(x \right)} + 180180 \sin^{24}{\left(x \right)} + 144144 \sin^{22}{\left(x \right)} + 120120 \sin^{20}{\left(x \right)} + 102960 \sin^{18}{\left(x \right)} + 90090 \sin^{16}{\left(x \right)} + 80080 \sin^{14}{\left(x \right)} + 72072 \sin^{12}{\left(x \right)} + 65520 \sin^{10}{\left(x \right)} + 60060 \sin^{8}{\left(x \right)} + 55440 \sin^{6}{\left(x \right)} + 51480 \sin^{4}{\left(x \right)} + 48048 \sin^{2}{\left(x \right)} + 45045}{1441440 \sin^{32}{\left(x \right)}} - \frac{\log{\left(\sin^{2}{\left(x \right)} - 1 \right)}}{2} + \log{\left(\sin{\left(x \right)} \right)}$$
Gráfica
Respuesta
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pi*I
oo - ----
2
$$\infty - \frac{i \pi}{2}$$
=
=
pi*I
oo - ----
2
$$\infty - \frac{i \pi}{2}$$
oo - pi*i/2
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.