Sr Examen
Integral de atan^2(x)/x^7 dx
Solución
Ha introducido
[src]
oo / | | 2 | atan (x) | -------- dx | 7 | x | / 1
$$\int\limits_{1}^{\infty} \frac{\operatorname{atan}^{2}{\left(x \right)}}{x^{7}}\, dx$$
Integral(atan(x)^2/x^7, (x, 1, oo))
Respuesta (Indefinida)
[src]
/ | | 2 / 2\ 2 2 | atan (x) 23*log\1 + x / atan (x) 1 4 23*log(x) atan(x) atan (x) atan(x) atan(x) | -------- dx = C - -------------- - -------- - ----- + ----- + --------- - ------- - -------- - ------- + ------- | 7 90 6 4 2 45 3*x 6 5 3 | x 60*x 45*x 6*x 15*x 9*x | /
$$\int \frac{\operatorname{atan}^{2}{\left(x \right)}}{x^{7}}\, dx = C + \frac{23 \log{\left(x \right)}}{45} - \frac{23 \log{\left(x^{2} + 1 \right)}}{90} - \frac{\operatorname{atan}^{2}{\left(x \right)}}{6} - \frac{\operatorname{atan}{\left(x \right)}}{3 x} + \frac{4}{45 x^{2}} + \frac{\operatorname{atan}{\left(x \right)}}{9 x^{3}} - \frac{1}{60 x^{4}} - \frac{\operatorname{atan}{\left(x \right)}}{15 x^{5}} - \frac{\operatorname{atan}^{2}{\left(x \right)}}{6 x^{6}}$$
Gráfica
Respuesta
[src]
2 13 pi 13*pi 23*log(2) - --- - --- + ----- + --------- 180 48 180 90
$$- \frac{\pi^{2}}{48} - \frac{13}{180} + \frac{23 \log{\left(2 \right)}}{90} + \frac{13 \pi}{180}$$
=
=
2 13 pi 13*pi 23*log(2) - --- - --- + ----- + --------- 180 48 180 90
$$- \frac{\pi^{2}}{48} - \frac{13}{180} + \frac{23 \log{\left(2 \right)}}{90} + \frac{13 \pi}{180}$$
-13/180 - pi^2/48 + 13*pi/180 + 23*log(2)/90
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.