Sr Examen
Integral de cos4x/sin^34x dx
Solución
Ha introducido
[src]
1 / | | cos(4*x) | -------- dx | 34 | sin (x) | / 0
$$\int\limits_{0}^{1} \frac{\cos{\left(4 x \right)}}{\sin^{34}{\left(x \right)}}\, dx$$
Integral(cos(4*x)/sin(x)^34, (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | 17 19 11 23 15 9 21 27 25 29 3 31 33 | cos(4*x) 13 7 5 12870*cot (x) 11440*cot (x) 4368*cot (x) 4368*cot (x) 2288*cot (x) 1820*cot (x) 1144*cot (x) 560*cot (x) 364*cot (x) 120*cot (x) 16*cot (x) 16*cot (x) cot (x) 268435456*cos(x) 134217728*cos(x) 33554432*cos(x) 20185088*cos(x) 18743296*cos(x) 16777216*cos(x) 14680064*cos(x) 7340032*cos(x) 1171456*cos(x) 585728*cos(x) 146432*cos(x) 46592*cos(x) 5824*cos(x) 224*cos(x) 8*cos(x) 8*cos(x) | -------- dx = C - cot(x) - 616*cot (x) - 80*cot (x) - 24*cot (x) - -------------- - -------------- - ------------- - ------------- - ------------- - ------------ - ------------- - ------------ - ------------ - ------------ - ---------- - ----------- - -------- - ----------------- - ------------------ - ------------------ - ------------------- - ------------------- - ----------------- - ----------------- - ------------------ - ------------------ - ----------------- - ----------------- - ---------------- - --------------- - -------------- - ------------ + ----------- | 34 17 19 11 23 3 9 3 27 5 29 3 31 33 4508102925*sin(x) 3 5 13 15 7 9 11 17 19 21 23 25 27 29 31 | sin (x) 4508102925*sin (x) 1502700975*sin (x) 1502700975*sin (x) 1502700975*sin (x) 901620585*sin (x) 901620585*sin (x) 500900325*sin (x) 100180065*sin (x) 53036505*sin (x) 13956975*sin (x) 4652325*sin (x) 606825*sin (x) 24273*sin (x) 899*sin (x) 31*sin (x) | /
$$\int \frac{\cos{\left(4 x \right)}}{\sin^{34}{\left(x \right)}}\, dx = C - \frac{\cot^{33}{\left(x \right)}}{33} - \frac{16 \cot^{31}{\left(x \right)}}{31} - \frac{120 \cot^{29}{\left(x \right)}}{29} - \frac{560 \cot^{27}{\left(x \right)}}{27} - \frac{364 \cot^{25}{\left(x \right)}}{5} - \frac{4368 \cot^{23}{\left(x \right)}}{23} - \frac{1144 \cot^{21}{\left(x \right)}}{3} - \frac{11440 \cot^{19}{\left(x \right)}}{19} - \frac{12870 \cot^{17}{\left(x \right)}}{17} - \frac{2288 \cot^{15}{\left(x \right)}}{3} - 616 \cot^{13}{\left(x \right)} - \frac{4368 \cot^{11}{\left(x \right)}}{11} - \frac{1820 \cot^{9}{\left(x \right)}}{9} - 80 \cot^{7}{\left(x \right)} - 24 \cot^{5}{\left(x \right)} - \frac{16 \cot^{3}{\left(x \right)}}{3} - \cot{\left(x \right)} - \frac{268435456 \cos{\left(x \right)}}{4508102925 \sin{\left(x \right)}} - \frac{134217728 \cos{\left(x \right)}}{4508102925 \sin^{3}{\left(x \right)}} - \frac{33554432 \cos{\left(x \right)}}{1502700975 \sin^{5}{\left(x \right)}} - \frac{16777216 \cos{\left(x \right)}}{901620585 \sin^{7}{\left(x \right)}} - \frac{14680064 \cos{\left(x \right)}}{901620585 \sin^{9}{\left(x \right)}} - \frac{7340032 \cos{\left(x \right)}}{500900325 \sin^{11}{\left(x \right)}} - \frac{20185088 \cos{\left(x \right)}}{1502700975 \sin^{13}{\left(x \right)}} - \frac{18743296 \cos{\left(x \right)}}{1502700975 \sin^{15}{\left(x \right)}} - \frac{1171456 \cos{\left(x \right)}}{100180065 \sin^{17}{\left(x \right)}} - \frac{585728 \cos{\left(x \right)}}{53036505 \sin^{19}{\left(x \right)}} - \frac{146432 \cos{\left(x \right)}}{13956975 \sin^{21}{\left(x \right)}} - \frac{46592 \cos{\left(x \right)}}{4652325 \sin^{23}{\left(x \right)}} - \frac{5824 \cos{\left(x \right)}}{606825 \sin^{25}{\left(x \right)}} - \frac{224 \cos{\left(x \right)}}{24273 \sin^{27}{\left(x \right)}} - \frac{8 \cos{\left(x \right)}}{899 \sin^{29}{\left(x \right)}} + \frac{8 \cos{\left(x \right)}}{31 \sin^{31}{\left(x \right)}}$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.