Sr Examen
Integral de cos^26x dx
Solución
Ha introducido
[src]
1 / | | 26 | cos (x) dx | / 0
$$\int\limits_{0}^{1} \cos^{26}{\left(x \right)}\, dx$$
Integral(cos(x)^26, (x, 0, 1))
Gráfica
Respuesta
[src]
25 23 21 19 17 7 9 11 13 5 15 3 1300075 cos (1)*sin(1) 25*cos (1)*sin(1) 575*cos (1)*sin(1) 805*cos (1)*sin(1) 15295*cos (1)*sin(1) 37145*cos (1)*sin(1) 37145*cos (1)*sin(1) 185725*cos (1)*sin(1) 185725*cos (1)*sin(1) 260015*cos (1)*sin(1) 260015*cos (1)*sin(1) 1300075*cos(1)*sin(1) 1300075*cos (1)*sin(1) ------- + --------------- + ------------------ + ------------------- + ------------------- + --------------------- + -------------------- + -------------------- + ---------------------- + ---------------------- + --------------------- + ---------------------- + --------------------- + ---------------------- 8388608 26 624 13728 18304 329472 524288 589824 3244032 3514368 3145728 5271552 8388608 12582912
$$\frac{\sin{\left(1 \right)} \cos^{25}{\left(1 \right)}}{26} + \frac{25 \sin{\left(1 \right)} \cos^{23}{\left(1 \right)}}{624} + \frac{575 \sin{\left(1 \right)} \cos^{21}{\left(1 \right)}}{13728} + \frac{805 \sin{\left(1 \right)} \cos^{19}{\left(1 \right)}}{18304} + \frac{15295 \sin{\left(1 \right)} \cos^{17}{\left(1 \right)}}{329472} + \frac{260015 \sin{\left(1 \right)} \cos^{15}{\left(1 \right)}}{5271552} + \frac{185725 \sin{\left(1 \right)} \cos^{13}{\left(1 \right)}}{3514368} + \frac{185725 \sin{\left(1 \right)} \cos^{11}{\left(1 \right)}}{3244032} + \frac{37145 \sin{\left(1 \right)} \cos^{9}{\left(1 \right)}}{589824} + \frac{37145 \sin{\left(1 \right)} \cos^{7}{\left(1 \right)}}{524288} + \frac{260015 \sin{\left(1 \right)} \cos^{5}{\left(1 \right)}}{3145728} + \frac{1300075 \sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{12582912} + \frac{1300075 \sin{\left(1 \right)} \cos{\left(1 \right)}}{8388608} + \frac{1300075}{8388608}$$
=
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25 23 21 19 17 7 9 11 13 5 15 3 1300075 cos (1)*sin(1) 25*cos (1)*sin(1) 575*cos (1)*sin(1) 805*cos (1)*sin(1) 15295*cos (1)*sin(1) 37145*cos (1)*sin(1) 37145*cos (1)*sin(1) 185725*cos (1)*sin(1) 185725*cos (1)*sin(1) 260015*cos (1)*sin(1) 260015*cos (1)*sin(1) 1300075*cos(1)*sin(1) 1300075*cos (1)*sin(1) ------- + --------------- + ------------------ + ------------------- + ------------------- + --------------------- + -------------------- + -------------------- + ---------------------- + ---------------------- + --------------------- + ---------------------- + --------------------- + ---------------------- 8388608 26 624 13728 18304 329472 524288 589824 3244032 3514368 3145728 5271552 8388608 12582912
$$\frac{\sin{\left(1 \right)} \cos^{25}{\left(1 \right)}}{26} + \frac{25 \sin{\left(1 \right)} \cos^{23}{\left(1 \right)}}{624} + \frac{575 \sin{\left(1 \right)} \cos^{21}{\left(1 \right)}}{13728} + \frac{805 \sin{\left(1 \right)} \cos^{19}{\left(1 \right)}}{18304} + \frac{15295 \sin{\left(1 \right)} \cos^{17}{\left(1 \right)}}{329472} + \frac{260015 \sin{\left(1 \right)} \cos^{15}{\left(1 \right)}}{5271552} + \frac{185725 \sin{\left(1 \right)} \cos^{13}{\left(1 \right)}}{3514368} + \frac{185725 \sin{\left(1 \right)} \cos^{11}{\left(1 \right)}}{3244032} + \frac{37145 \sin{\left(1 \right)} \cos^{9}{\left(1 \right)}}{589824} + \frac{37145 \sin{\left(1 \right)} \cos^{7}{\left(1 \right)}}{524288} + \frac{260015 \sin{\left(1 \right)} \cos^{5}{\left(1 \right)}}{3145728} + \frac{1300075 \sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{12582912} + \frac{1300075 \sin{\left(1 \right)} \cos{\left(1 \right)}}{8388608} + \frac{1300075}{8388608}$$
1300075/8388608 + cos(1)^25*sin(1)/26 + 25*cos(1)^23*sin(1)/624 + 575*cos(1)^21*sin(1)/13728 + 805*cos(1)^19*sin(1)/18304 + 15295*cos(1)^17*sin(1)/329472 + 37145*cos(1)^7*sin(1)/524288 + 37145*cos(1)^9*sin(1)/589824 + 185725*cos(1)^11*sin(1)/3244032 + 185725*cos(1)^13*sin(1)/3514368 + 260015*cos(1)^5*sin(1)/3145728 + 260015*cos(1)^15*sin(1)/5271552 + 1300075*cos(1)*sin(1)/8388608 + 1300075*cos(1)^3*sin(1)/12582912
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.