Sr Examen
Integral de cos(x)^3*1/sin(2x)^6 dx
Solución
Ha introducido
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1 / | | 3 | cos (x) | --------- dx | 6 | sin (2*x) | / 0
$$\int\limits_{0}^{1} \frac{\cos^{3}{\left(x \right)}}{\sin^{6}{\left(2 x \right)}}\, dx$$
Integral(cos(x)^3/sin(2*x)^6, (x, 0, 1))
Respuesta (Indefinida)
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/ | | 3 6 2 4 8 4 2 6 | cos (x) 7*log(-1 + sin(x)) 7*log(1 + sin(x)) 8 - 525*sin (x) + 24*sin (x) + 168*sin (x) + 315*sin (x) 8 - 175*sin (x) + 56*sin (x) + 105*sin (x) | --------- dx = C - ------------------ + ----------------- - -------------------------------------------------------- + ------------------------------------------- | 6 256 256 / 7 5 9 \ / 5 3 7 \ | sin (2*x) 64*\- 80*sin (x) + 40*sin (x) + 40*sin (x)/ 64*\- 48*sin (x) + 24*sin (x) + 24*sin (x)/ | /
$$\int \frac{\cos^{3}{\left(x \right)}}{\sin^{6}{\left(2 x \right)}}\, dx = C - \frac{7 \log{\left(\sin{\left(x \right)} - 1 \right)}}{256} + \frac{7 \log{\left(\sin{\left(x \right)} + 1 \right)}}{256} - \frac{315 \sin^{8}{\left(x \right)} - 525 \sin^{6}{\left(x \right)} + 168 \sin^{4}{\left(x \right)} + 24 \sin^{2}{\left(x \right)} + 8}{64 \left(40 \sin^{9}{\left(x \right)} - 80 \sin^{7}{\left(x \right)} + 40 \sin^{5}{\left(x \right)}\right)} + \frac{105 \sin^{6}{\left(x \right)} - 175 \sin^{4}{\left(x \right)} + 56 \sin^{2}{\left(x \right)} + 8}{64 \left(24 \sin^{7}{\left(x \right)} - 48 \sin^{5}{\left(x \right)} + 24 \sin^{3}{\left(x \right)}\right)}$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.