Sr Examen
Integral de -32cos4x/sin^34x dx
Solución
Ha introducido
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1 / | | -32*cos(4*x) | ------------ dx | 34 | sin (x) | / 0
$$\int\limits_{0}^{1} \frac{\left(-1\right) 32 \cos{\left(4 x \right)}}{\sin^{34}{\left(x \right)}}\, dx$$
Integral((-32*cos(4*x))/sin(x)^34, (x, 0, 1))
Respuesta (Indefinida)
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/ | 33 3 31 29 25 27 21 9 15 11 23 19 17 | -32*cos(4*x) 5 7 13 32*cot (x) 512*cot (x) 512*cot (x) 3840*cot (x) 11648*cot (x) 17920*cot (x) 36608*cot (x) 58240*cot (x) 73216*cot (x) 139776*cot (x) 139776*cot (x) 366080*cot (x) 411840*cot (x) 256*cos(x) 256*cos(x) 7168*cos(x) 186368*cos(x) 1490944*cos(x) 4685824*cos(x) 18743296*cos(x) 37486592*cos(x) 234881024*cos(x) 469762048*cos(x) 536870912*cos(x) 599785472*cos(x) 645922816*cos(x) 1073741824*cos(x) 4294967296*cos(x) 8589934592*cos(x) | ------------ dx = C + 32*cot(x) + 768*cot (x) + 2560*cot (x) + 19712*cot (x) + ----------- + ----------- + ------------ + ------------- + -------------- + -------------- + -------------- + ------------- + -------------- + --------------- + --------------- + --------------- + --------------- - ----------- + ------------ + -------------- + --------------- + ---------------- + ----------------- + ----------------- + ------------------ + ------------------ + ----------------- + ----------------- + ------------------- + ------------------- + ------------------ + ------------------ + ----------------- | 34 33 3 31 29 5 27 3 9 3 11 23 19 17 31 29 27 25 23 21 19 17 11 9 7 15 13 5 3 4508102925*sin(x) | sin (x) 31*sin (x) 899*sin (x) 24273*sin (x) 606825*sin (x) 4652325*sin (x) 13956975*sin (x) 53036505*sin (x) 100180065*sin (x) 500900325*sin (x) 901620585*sin (x) 901620585*sin (x) 1502700975*sin (x) 1502700975*sin (x) 1502700975*sin (x) 4508102925*sin (x) | /
$$\int \frac{\left(-1\right) 32 \cos{\left(4 x \right)}}{\sin^{34}{\left(x \right)}}\, dx = C + \frac{32 \cot^{33}{\left(x \right)}}{33} + \frac{512 \cot^{31}{\left(x \right)}}{31} + \frac{3840 \cot^{29}{\left(x \right)}}{29} + \frac{17920 \cot^{27}{\left(x \right)}}{27} + \frac{11648 \cot^{25}{\left(x \right)}}{5} + \frac{139776 \cot^{23}{\left(x \right)}}{23} + \frac{36608 \cot^{21}{\left(x \right)}}{3} + \frac{366080 \cot^{19}{\left(x \right)}}{19} + \frac{411840 \cot^{17}{\left(x \right)}}{17} + \frac{73216 \cot^{15}{\left(x \right)}}{3} + 19712 \cot^{13}{\left(x \right)} + \frac{139776 \cot^{11}{\left(x \right)}}{11} + \frac{58240 \cot^{9}{\left(x \right)}}{9} + 2560 \cot^{7}{\left(x \right)} + 768 \cot^{5}{\left(x \right)} + \frac{512 \cot^{3}{\left(x \right)}}{3} + 32 \cot{\left(x \right)} + \frac{8589934592 \cos{\left(x \right)}}{4508102925 \sin{\left(x \right)}} + \frac{4294967296 \cos{\left(x \right)}}{4508102925 \sin^{3}{\left(x \right)}} + \frac{1073741824 \cos{\left(x \right)}}{1502700975 \sin^{5}{\left(x \right)}} + \frac{536870912 \cos{\left(x \right)}}{901620585 \sin^{7}{\left(x \right)}} + \frac{469762048 \cos{\left(x \right)}}{901620585 \sin^{9}{\left(x \right)}} + \frac{234881024 \cos{\left(x \right)}}{500900325 \sin^{11}{\left(x \right)}} + \frac{645922816 \cos{\left(x \right)}}{1502700975 \sin^{13}{\left(x \right)}} + \frac{599785472 \cos{\left(x \right)}}{1502700975 \sin^{15}{\left(x \right)}} + \frac{37486592 \cos{\left(x \right)}}{100180065 \sin^{17}{\left(x \right)}} + \frac{18743296 \cos{\left(x \right)}}{53036505 \sin^{19}{\left(x \right)}} + \frac{4685824 \cos{\left(x \right)}}{13956975 \sin^{21}{\left(x \right)}} + \frac{1490944 \cos{\left(x \right)}}{4652325 \sin^{23}{\left(x \right)}} + \frac{186368 \cos{\left(x \right)}}{606825 \sin^{25}{\left(x \right)}} + \frac{7168 \cos{\left(x \right)}}{24273 \sin^{27}{\left(x \right)}} + \frac{256 \cos{\left(x \right)}}{899 \sin^{29}{\left(x \right)}} - \frac{256 \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.