Sr Examen
Integral de 2cos2x\(sin²2x) dx
Solución
Ha introducido
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1 / | | 2*cos(2*x) | ---------- dx | 22 | sin (x) | / 0
$$\int\limits_{0}^{1} \frac{2 \cos{\left(2 x \right)}}{\sin^{22}{\left(x \right)}}\, dx$$
Integral((2*cos(2*x))/sin(x)^22, (x, 0, 1))
Respuesta (Indefinida)
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/ | 21 3 19 17 9 7 13 11 | 2*cos(2*x) 15 5 2*cot (x) 20*cot (x) 20*cot (x) 90*cot (x) 140*cot (x) 240*cot (x) 420*cot (x) 504*cot (x) 4*cos(x) 4*cos(x) 24*cos(x) 128*cos(x) 256*cos(x) 2048*cos(x) 3072*cos(x) 16384*cos(x) 32768*cos(x) 131072*cos(x) 262144*cos(x) | ---------- dx = C + 2*cot(x) + 16*cot (x) + 18*cot (x) + ---------- + ---------- + ----------- + ----------- + ----------- + ----------- + ------------ + ------------ - ----------- + ------------ + ------------- + -------------- + -------------- + -------------- + --------------- + -------------- + --------------- + --------------- + -------------- | 22 21 3 19 17 3 7 13 11 21 19 17 15 13 9 11 7 5 3 4849845*sin(x) | sin (x) 21*sin (x) 399*sin (x) 2261*sin (x) 11305*sin (x) 20995*sin (x) 138567*sin (x) 230945*sin (x) 969969*sin (x) 1616615*sin (x) 4849845*sin (x) | /
$$\int \frac{2 \cos{\left(2 x \right)}}{\sin^{22}{\left(x \right)}}\, dx = C + \frac{2 \cot^{21}{\left(x \right)}}{21} + \frac{20 \cot^{19}{\left(x \right)}}{19} + \frac{90 \cot^{17}{\left(x \right)}}{17} + 16 \cot^{15}{\left(x \right)} + \frac{420 \cot^{13}{\left(x \right)}}{13} + \frac{504 \cot^{11}{\left(x \right)}}{11} + \frac{140 \cot^{9}{\left(x \right)}}{3} + \frac{240 \cot^{7}{\left(x \right)}}{7} + 18 \cot^{5}{\left(x \right)} + \frac{20 \cot^{3}{\left(x \right)}}{3} + 2 \cot{\left(x \right)} + \frac{262144 \cos{\left(x \right)}}{4849845 \sin{\left(x \right)}} + \frac{131072 \cos{\left(x \right)}}{4849845 \sin^{3}{\left(x \right)}} + \frac{32768 \cos{\left(x \right)}}{1616615 \sin^{5}{\left(x \right)}} + \frac{16384 \cos{\left(x \right)}}{969969 \sin^{7}{\left(x \right)}} + \frac{2048 \cos{\left(x \right)}}{138567 \sin^{9}{\left(x \right)}} + \frac{3072 \cos{\left(x \right)}}{230945 \sin^{11}{\left(x \right)}} + \frac{256 \cos{\left(x \right)}}{20995 \sin^{13}{\left(x \right)}} + \frac{128 \cos{\left(x \right)}}{11305 \sin^{15}{\left(x \right)}} + \frac{24 \cos{\left(x \right)}}{2261 \sin^{17}{\left(x \right)}} + \frac{4 \cos{\left(x \right)}}{399 \sin^{19}{\left(x \right)}} - \frac{4 \cos{\left(x \right)}}{21 \sin^{21}{\left(x \right)}}$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.