Sr Examen
Integral de 2*(1/x+1)^(13/2) dx
Solución
Ha introducido
[src]
5 / | | 13/2 | /1 \ | 2*|- + 1| dx | \x / | / 1
$$\int\limits_{1}^{5} 2 \left(1 + \frac{1}{x}\right)^{\frac{13}{2}}\, dx$$
Integral(2*(1/x + 1)^(13/2), (x, 1, 5))
Respuesta (Indefinida)
[src]
/ | | 13/2 _______ 3/2 / _______\ / _______\ 15/2 13/2 17/2 11/2 19/2 _______ _______ _______ 9/2 21/2 _______ 5/2 7/2 7/2 13/2 11/2 31/2 9/2 11/2 13/2 29/2 15/2 27/2 17/2 25/2 19/2 23/2 21/2 5 _______ 6 _______ 4 _______ 7 _______ 3 _______ 8 _______ 10 _______ 11 _______ 9 _______ 2 _______ 12 _______ 13 _______ 3 _______ 4 _______ 2 _______ _______ _______ 14 _______ 5 _______ 2 _______ _______ 3 _______ 5 _______ 4 _______ 15 _______ 6 _______ _______ 2 _______ 3 _______ 10 _______ 9 _______ 6 _______ 8 _______ 7 _______ | /1 \ / 1 / 1\ | / 1 | / ___\ | / 1 | 7680*x 5760*x 5760*x 2304*x 2304*x 1260*\/ 1 + x 900*\/ 1 + x 840*\/ 1 + x 384*x 384*x 240*\/ 1 + x 160*x 160*x ___ _______ 480*x 480*x 512*x 512*x 1440*x 1440*x 5120*x 5120*x 23040*x 23040*x 61440*x 61440*x 107520*x 107520*x 129024*x 334312*x *\/ 1 + x 282920*x *\/ 1 + x 275864*x *\/ 1 + x 172920*x *\/ 1 + x 156092*x *\/ 1 + x 95964*x *\/ 1 + x 93764*x *\/ 1 + x 83980*x *\/ 1 + x 83028*x *\/ 1 + x 57940*x *\/ 1 + x 51680*x *\/ 1 + x 20672*x *\/ 1 + x 17928*x *\/ 1 + x 13608*x *\/ 1 + x 13176*x *\/ 1 + x 12740*x*\/ 1 + x 5160*x*\/ 1 + x 4864*x *\/ 1 + x 4536*x *\/ 1 + x 3000*x *\/ 1 + x 2880*x*\/ 1 + x 1200*x *\/ 1 + x 1200*x *\/ 1 + x 900*x *\/ 1 + x 512*x *\/ 1 + x 480*x *\/ 1 + x 320*x*\/ 1 + x 80*x *\/ 1 + x 160*x *\/ 1 + x 384*x *\/ 1 + x 2112*x *\/ 1 + x 2520*x *\/ 1 + x 4752*x *\/ 1 + x 5544*x *\/ 1 + x | 2*|- + 1| dx = C - 24* / 1 + - - 20*|1 + -| - 12*log|-1 + / 1 + - | + 2*asinh\\/ x / + 12*log|1 + / 1 + - | - ------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------- - 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------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------- | \x / \/ x \ x/ \ \/ x / \ \/ x / 9/2 21/2 11/2 19/2 13/2 17/2 15/2 9/2 21/2 11/2 19/2 13/2 17/2 15/2 9/2 21/2 11/2 19/2 13/2 17/2 15/2 9/2 21/2 11/2 19/2 13/2 17/2 15/2 9/2 21/2 11/2 19/2 13/2 17/2 15/2 11/2 31/2 13/2 29/2 15/2 27/2 17/2 25/2 19/2 23/2 21/2 7/2 13/2 9/2 11/2 9/2 21/2 11/2 19/2 13/2 17/2 15/2 9/2 21/2 11/2 19/2 13/2 17/2 15/2 9/2 21/2 11/2 19/2 13/2 17/2 15/2 5/2 7/2 5/2 7/2 5/2 7/2 7/2 13/2 9/2 11/2 7/2 13/2 9/2 11/2 11/2 31/2 13/2 29/2 15/2 27/2 17/2 25/2 19/2 23/2 21/2 11/2 31/2 13/2 29/2 15/2 27/2 17/2 25/2 19/2 23/2 21/2 7/2 13/2 9/2 11/2 7/2 13/2 9/2 11/2 11/2 31/2 13/2 29/2 15/2 27/2 17/2 25/2 19/2 23/2 21/2 11/2 31/2 13/2 29/2 15/2 27/2 17/2 25/2 19/2 23/2 21/2 11/2 31/2 13/2 29/2 15/2 27/2 17/2 25/2 19/2 23/2 21/2 11/2 31/2 13/2 29/2 15/2 27/2 17/2 25/2 19/2 23/2 21/2 11/2 31/2 13/2 29/2 15/2 27/2 17/2 25/2 19/2 23/2 21/2 11/2 31/2 13/2 29/2 15/2 27/2 17/2 25/2 19/2 23/2 21/2 11/2 31/2 13/2 29/2 15/2 27/2 17/2 25/2 19/2 23/2 21/2 11/2 31/2 13/2 29/2 15/2 27/2 17/2 25/2 19/2 23/2 21/2 11/2 31/2 13/2 29/2 15/2 27/2 17/2 25/2 19/2 23/2 21/2 11/2 31/2 13/2 29/2 15/2 27/2 17/2 25/2 19/2 23/2 21/2 11/2 31/2 13/2 29/2 15/2 27/2 17/2 25/2 19/2 23/2 21/2 11/2 31/2 13/2 29/2 15/2 27/2 17/2 25/2 19/2 23/2 21/2 11/2 31/2 13/2 29/2 15/2 27/2 17/2 25/2 19/2 23/2 21/2 11/2 31/2 13/2 29/2 15/2 27/2 17/2 25/2 19/2 23/2 21/2 11/2 31/2 13/2 29/2 15/2 27/2 17/2 25/2 19/2 23/2 21/2 11/2 31/2 13/2 29/2 15/2 27/2 17/2 25/2 19/2 23/2 21/2 11/2 31/2 13/2 29/2 15/2 27/2 17/2 25/2 19/2 23/2 21/2 11/2 31/2 13/2 29/2 15/2 27/2 17/2 25/2 19/2 23/2 21/2 11/2 31/2 13/2 29/2 15/2 27/2 17/2 25/2 19/2 23/2 21/2 11/2 31/2 13/2 29/2 15/2 27/2 17/2 25/2 19/2 23/2 21/2 11/2 31/2 13/2 29/2 15/2 27/2 17/2 25/2 19/2 23/2 21/2 9/2 21/2 11/2 19/2 13/2 17/2 15/2 9/2 21/2 11/2 19/2 13/2 17/2 15/2 9/2 21/2 11/2 19/2 13/2 17/2 15/2 11/2 31/2 13/2 29/2 15/2 27/2 17/2 25/2 19/2 23/2 21/2 9/2 21/2 11/2 19/2 13/2 17/2 15/2 11/2 31/2 13/2 29/2 15/2 27/2 17/2 25/2 19/2 23/2 21/2 9/2 21/2 11/2 19/2 13/2 17/2 15/2 7/2 13/2 9/2 11/2 7/2 13/2 9/2 11/2 7/2 13/2 9/2 11/2 7/2 13/2 9/2 11/2 7/2 13/2 9/2 11/2 11/2 31/2 13/2 29/2 15/2 27/2 17/2 25/2 19/2 23/2 21/2 7/2 13/2 9/2 11/2 5/2 7/2 5/2 7/2 5/2 7/2 9/2 21/2 11/2 19/2 13/2 17/2 15/2 9/2 21/2 11/2 19/2 13/2 17/2 15/2 9/2 21/2 11/2 19/2 13/2 17/2 15/2 9/2 21/2 11/2 19/2 13/2 17/2 15/2 9/2 21/2 11/2 19/2 13/2 17/2 15/2 | 315*x + 315*x + 1890*x + 1890*x + 4725*x + 4725*x + 6300*x 315*x + 315*x + 1890*x + 1890*x + 4725*x + 4725*x + 6300*x 315*x + 315*x + 1890*x + 1890*x + 4725*x + 4725*x + 6300*x 315*x + 315*x + 1890*x + 1890*x + 4725*x + 4725*x + 6300*x 315*x + 315*x + 1890*x + 1890*x + 4725*x + 4725*x + 6300*x 3465*x + 3465*x + 34650*x + 34650*x + 155925*x + 155925*x + 415800*x + 415800*x + 727650*x + 727650*x + 873180*x 105*x + 105*x + 315*x + 315*x 315*x + 315*x + 1890*x + 1890*x + 4725*x + 4725*x + 6300*x 315*x + 315*x + 1890*x + 1890*x + 4725*x + 4725*x + 6300*x 315*x + 315*x + 1890*x + 1890*x + 4725*x + 4725*x + 6300*x 15*x + 15*x 15*x + 15*x 15*x + 15*x 105*x + 105*x + 315*x + 315*x 105*x + 105*x + 315*x + 315*x 3465*x + 3465*x + 34650*x + 34650*x + 155925*x + 155925*x + 415800*x + 415800*x + 727650*x + 727650*x + 873180*x 3465*x + 3465*x + 34650*x + 34650*x + 155925*x + 155925*x + 415800*x + 415800*x + 727650*x + 727650*x + 873180*x 105*x + 105*x + 315*x + 315*x 105*x + 105*x + 315*x + 315*x 3465*x + 3465*x + 34650*x + 34650*x + 155925*x + 155925*x + 415800*x + 415800*x + 727650*x + 727650*x + 873180*x 3465*x + 3465*x + 34650*x + 34650*x + 155925*x + 155925*x + 415800*x + 415800*x + 727650*x + 727650*x + 873180*x 3465*x + 3465*x + 34650*x + 34650*x + 155925*x + 155925*x + 415800*x + 415800*x + 727650*x + 727650*x + 873180*x 3465*x + 3465*x + 34650*x + 34650*x + 155925*x + 155925*x + 415800*x + 415800*x + 727650*x + 727650*x + 873180*x 3465*x + 3465*x + 34650*x + 34650*x + 155925*x + 155925*x + 415800*x + 415800*x + 727650*x + 727650*x + 873180*x 3465*x + 3465*x + 34650*x + 34650*x + 155925*x + 155925*x + 415800*x + 415800*x + 727650*x + 727650*x + 873180*x 3465*x + 3465*x + 34650*x + 34650*x + 155925*x + 155925*x + 415800*x + 415800*x + 727650*x + 727650*x + 873180*x 3465*x + 3465*x + 34650*x + 34650*x + 155925*x + 155925*x + 415800*x + 415800*x + 727650*x + 727650*x + 873180*x 3465*x + 3465*x + 34650*x + 34650*x + 155925*x + 155925*x + 415800*x + 415800*x + 727650*x + 727650*x + 873180*x 3465*x + 3465*x + 34650*x + 34650*x + 155925*x + 155925*x + 415800*x + 415800*x + 727650*x + 727650*x + 873180*x 3465*x + 3465*x + 34650*x + 34650*x + 155925*x + 155925*x + 415800*x + 415800*x + 727650*x + 727650*x + 873180*x 3465*x + 3465*x + 34650*x + 34650*x + 155925*x + 155925*x + 415800*x + 415800*x + 727650*x + 727650*x + 873180*x 3465*x + 3465*x + 34650*x + 34650*x + 155925*x + 155925*x + 415800*x + 415800*x + 727650*x + 727650*x + 873180*x 3465*x + 3465*x + 34650*x + 34650*x + 155925*x + 155925*x + 415800*x + 415800*x + 727650*x + 727650*x + 873180*x 3465*x + 3465*x + 34650*x + 34650*x + 155925*x + 155925*x + 415800*x + 415800*x + 727650*x + 727650*x + 873180*x 3465*x + 3465*x + 34650*x + 34650*x + 155925*x + 155925*x + 415800*x + 415800*x + 727650*x + 727650*x + 873180*x 3465*x + 3465*x + 34650*x + 34650*x + 155925*x + 155925*x + 415800*x + 415800*x + 727650*x + 727650*x + 873180*x 3465*x + 3465*x + 34650*x + 34650*x + 155925*x + 155925*x + 415800*x + 415800*x + 727650*x + 727650*x + 873180*x 3465*x + 3465*x + 34650*x + 34650*x + 155925*x + 155925*x + 415800*x + 415800*x + 727650*x + 727650*x + 873180*x 3465*x + 3465*x + 34650*x + 34650*x + 155925*x + 155925*x + 415800*x + 415800*x + 727650*x + 727650*x + 873180*x 3465*x + 3465*x + 34650*x + 34650*x + 155925*x + 155925*x + 415800*x + 415800*x + 727650*x + 727650*x + 873180*x 315*x + 315*x + 1890*x + 1890*x + 4725*x + 4725*x + 6300*x 315*x + 315*x + 1890*x + 1890*x + 4725*x + 4725*x + 6300*x 315*x + 315*x + 1890*x + 1890*x + 4725*x + 4725*x + 6300*x 3465*x + 3465*x + 34650*x + 34650*x + 155925*x + 155925*x + 415800*x + 415800*x + 727650*x + 727650*x + 873180*x 315*x + 315*x + 1890*x + 1890*x + 4725*x + 4725*x + 6300*x 3465*x + 3465*x + 34650*x + 34650*x + 155925*x + 155925*x + 415800*x + 415800*x + 727650*x + 727650*x + 873180*x 315*x + 315*x + 1890*x + 1890*x + 4725*x + 4725*x + 6300*x 105*x + 105*x + 315*x + 315*x 105*x + 105*x + 315*x + 315*x 105*x + 105*x + 315*x + 315*x 105*x + 105*x + 315*x + 315*x 105*x + 105*x + 315*x + 315*x 3465*x + 3465*x + 34650*x + 34650*x + 155925*x + 155925*x + 415800*x + 415800*x + 727650*x + 727650*x + 873180*x 105*x + 105*x + 315*x + 315*x 15*x + 15*x 15*x + 15*x 15*x + 15*x 315*x + 315*x + 1890*x + 1890*x + 4725*x + 4725*x + 6300*x 315*x + 315*x + 1890*x + 1890*x + 4725*x + 4725*x + 6300*x 315*x + 315*x + 1890*x + 1890*x + 4725*x + 4725*x + 6300*x 315*x + 315*x + 1890*x + 1890*x + 4725*x + 4725*x + 6300*x 315*x + 315*x + 1890*x + 1890*x + 4725*x + 4725*x + 6300*x /
$$\int 2 \left(1 + \frac{1}{x}\right)^{\frac{13}{2}}\, dx = C + \frac{512 x^{\frac{31}{2}}}{3465 x^{\frac{31}{2}} + 34650 x^{\frac{29}{2}} + 155925 x^{\frac{27}{2}} + 415800 x^{\frac{25}{2}} + 727650 x^{\frac{23}{2}} + 873180 x^{\frac{21}{2}} + 727650 x^{\frac{19}{2}} + 415800 x^{\frac{17}{2}} + 155925 x^{\frac{15}{2}} + 34650 x^{\frac{13}{2}} + 3465 x^{\frac{11}{2}}} + \frac{5120 x^{\frac{29}{2}}}{3465 x^{\frac{31}{2}} + 34650 x^{\frac{29}{2}} + 155925 x^{\frac{27}{2}} + 415800 x^{\frac{25}{2}} + 727650 x^{\frac{23}{2}} + 873180 x^{\frac{21}{2}} + 727650 x^{\frac{19}{2}} + 415800 x^{\frac{17}{2}} + 155925 x^{\frac{15}{2}} + 34650 x^{\frac{13}{2}} + 3465 x^{\frac{11}{2}}} + \frac{23040 x^{\frac{27}{2}}}{3465 x^{\frac{31}{2}} + 34650 x^{\frac{29}{2}} + 155925 x^{\frac{27}{2}} + 415800 x^{\frac{25}{2}} + 727650 x^{\frac{23}{2}} + 873180 x^{\frac{21}{2}} + 727650 x^{\frac{19}{2}} + 415800 x^{\frac{17}{2}} + 155925 x^{\frac{15}{2}} + 34650 x^{\frac{13}{2}} + 3465 x^{\frac{11}{2}}} + \frac{61440 x^{\frac{25}{2}}}{3465 x^{\frac{31}{2}} + 34650 x^{\frac{29}{2}} + 155925 x^{\frac{27}{2}} + 415800 x^{\frac{25}{2}} + 727650 x^{\frac{23}{2}} + 873180 x^{\frac{21}{2}} + 727650 x^{\frac{19}{2}} + 415800 x^{\frac{17}{2}} + 155925 x^{\frac{15}{2}} + 34650 x^{\frac{13}{2}} + 3465 x^{\frac{11}{2}}} + \frac{107520 x^{\frac{23}{2}}}{3465 x^{\frac{31}{2}} + 34650 x^{\frac{29}{2}} + 155925 x^{\frac{27}{2}} + 415800 x^{\frac{25}{2}} + 727650 x^{\frac{23}{2}} + 873180 x^{\frac{21}{2}} + 727650 x^{\frac{19}{2}} + 415800 x^{\frac{17}{2}} + 155925 x^{\frac{15}{2}} + 34650 x^{\frac{13}{2}} + 3465 x^{\frac{11}{2}}} + \frac{129024 x^{\frac{21}{2}}}{3465 x^{\frac{31}{2}} + 34650 x^{\frac{29}{2}} + 155925 x^{\frac{27}{2}} + 415800 x^{\frac{25}{2}} + 727650 x^{\frac{23}{2}} + 873180 x^{\frac{21}{2}} + 727650 x^{\frac{19}{2}} + 415800 x^{\frac{17}{2}} + 155925 x^{\frac{15}{2}} + 34650 x^{\frac{13}{2}} + 3465 x^{\frac{11}{2}}} - \frac{384 x^{\frac{21}{2}}}{315 x^{\frac{21}{2}} + 1890 x^{\frac{19}{2}} + 4725 x^{\frac{17}{2}} + 6300 x^{\frac{15}{2}} + 4725 x^{\frac{13}{2}} + 1890 x^{\frac{11}{2}} + 315 x^{\frac{9}{2}}} + \frac{107520 x^{\frac{19}{2}}}{3465 x^{\frac{31}{2}} + 34650 x^{\frac{29}{2}} + 155925 x^{\frac{27}{2}} + 415800 x^{\frac{25}{2}} + 727650 x^{\frac{23}{2}} + 873180 x^{\frac{21}{2}} + 727650 x^{\frac{19}{2}} + 415800 x^{\frac{17}{2}} + 155925 x^{\frac{15}{2}} + 34650 x^{\frac{13}{2}} + 3465 x^{\frac{11}{2}}} - \frac{2304 x^{\frac{19}{2}}}{315 x^{\frac{21}{2}} + 1890 x^{\frac{19}{2}} + 4725 x^{\frac{17}{2}} + 6300 x^{\frac{15}{2}} + 4725 x^{\frac{13}{2}} + 1890 x^{\frac{11}{2}} + 315 x^{\frac{9}{2}}} + \frac{61440 x^{\frac{17}{2}}}{3465 x^{\frac{31}{2}} + 34650 x^{\frac{29}{2}} + 155925 x^{\frac{27}{2}} + 415800 x^{\frac{25}{2}} + 727650 x^{\frac{23}{2}} + 873180 x^{\frac{21}{2}} + 727650 x^{\frac{19}{2}} + 415800 x^{\frac{17}{2}} + 155925 x^{\frac{15}{2}} + 34650 x^{\frac{13}{2}} + 3465 x^{\frac{11}{2}}} - \frac{5760 x^{\frac{17}{2}}}{315 x^{\frac{21}{2}} + 1890 x^{\frac{19}{2}} + 4725 x^{\frac{17}{2}} + 6300 x^{\frac{15}{2}} + 4725 x^{\frac{13}{2}} + 1890 x^{\frac{11}{2}} + 315 x^{\frac{9}{2}}} + \frac{23040 x^{\frac{15}{2}}}{3465 x^{\frac{31}{2}} + 34650 x^{\frac{29}{2}} + 155925 x^{\frac{27}{2}} + 415800 x^{\frac{25}{2}} + 727650 x^{\frac{23}{2}} + 873180 x^{\frac{21}{2}} + 727650 x^{\frac{19}{2}} + 415800 x^{\frac{17}{2}} + 155925 x^{\frac{15}{2}} + 34650 x^{\frac{13}{2}} + 3465 x^{\frac{11}{2}}} - \frac{7680 x^{\frac{15}{2}}}{315 x^{\frac{21}{2}} + 1890 x^{\frac{19}{2}} + 4725 x^{\frac{17}{2}} + 6300 x^{\frac{15}{2}} + 4725 x^{\frac{13}{2}} + 1890 x^{\frac{11}{2}} + 315 x^{\frac{9}{2}}} + \frac{5120 x^{\frac{13}{2}}}{3465 x^{\frac{31}{2}} + 34650 x^{\frac{29}{2}} + 155925 x^{\frac{27}{2}} + 415800 x^{\frac{25}{2}} + 727650 x^{\frac{23}{2}} + 873180 x^{\frac{21}{2}} + 727650 x^{\frac{19}{2}} + 415800 x^{\frac{17}{2}} + 155925 x^{\frac{15}{2}} + 34650 x^{\frac{13}{2}} + 3465 x^{\frac{11}{2}}} - \frac{5760 x^{\frac{13}{2}}}{315 x^{\frac{21}{2}} + 1890 x^{\frac{19}{2}} + 4725 x^{\frac{17}{2}} + 6300 x^{\frac{15}{2}} + 4725 x^{\frac{13}{2}} + 1890 x^{\frac{11}{2}} + 315 x^{\frac{9}{2}}} + \frac{480 x^{\frac{13}{2}}}{105 x^{\frac{13}{2}} + 315 x^{\frac{11}{2}} + 315 x^{\frac{9}{2}} + 105 x^{\frac{7}{2}}} + \frac{512 x^{\frac{11}{2}}}{3465 x^{\frac{31}{2}} + 34650 x^{\frac{29}{2}} + 155925 x^{\frac{27}{2}} + 415800 x^{\frac{25}{2}} + 727650 x^{\frac{23}{2}} + 873180 x^{\frac{21}{2}} + 727650 x^{\frac{19}{2}} + 415800 x^{\frac{17}{2}} + 155925 x^{\frac{15}{2}} + 34650 x^{\frac{13}{2}} + 3465 x^{\frac{11}{2}}} - \frac{2304 x^{\frac{11}{2}}}{315 x^{\frac{21}{2}} + 1890 x^{\frac{19}{2}} + 4725 x^{\frac{17}{2}} + 6300 x^{\frac{15}{2}} + 4725 x^{\frac{13}{2}} + 1890 x^{\frac{11}{2}} + 315 x^{\frac{9}{2}}} + \frac{1440 x^{\frac{11}{2}}}{105 x^{\frac{13}{2}} + 315 x^{\frac{11}{2}} + 315 x^{\frac{9}{2}} + 105 x^{\frac{7}{2}}} - \frac{384 x^{\frac{9}{2}}}{315 x^{\frac{21}{2}} + 1890 x^{\frac{19}{2}} + 4725 x^{\frac{17}{2}} + 6300 x^{\frac{15}{2}} + 4725 x^{\frac{13}{2}} + 1890 x^{\frac{11}{2}} + 315 x^{\frac{9}{2}}} + \frac{1440 x^{\frac{9}{2}}}{105 x^{\frac{13}{2}} + 315 x^{\frac{11}{2}} + 315 x^{\frac{9}{2}} + 105 x^{\frac{7}{2}}} + \frac{480 x^{\frac{7}{2}}}{105 x^{\frac{13}{2}} + 315 x^{\frac{11}{2}} + 315 x^{\frac{9}{2}} + 105 x^{\frac{7}{2}}} - \frac{160 x^{\frac{7}{2}}}{15 x^{\frac{7}{2}} + 15 x^{\frac{5}{2}}} - \frac{160 x^{\frac{5}{2}}}{15 x^{\frac{7}{2}} + 15 x^{\frac{5}{2}}} + 2 \sqrt{x} \sqrt{x + 1} - \frac{512 x^{15} \sqrt{x + 1}}{3465 x^{\frac{31}{2}} + 34650 x^{\frac{29}{2}} + 155925 x^{\frac{27}{2}} + 415800 x^{\frac{25}{2}} + 727650 x^{\frac{23}{2}} + 873180 x^{\frac{21}{2}} + 727650 x^{\frac{19}{2}} + 415800 x^{\frac{17}{2}} + 155925 x^{\frac{15}{2}} + 34650 x^{\frac{13}{2}} + 3465 x^{\frac{11}{2}}} - \frac{4864 x^{14} \sqrt{x + 1}}{3465 x^{\frac{31}{2}} + 34650 x^{\frac{29}{2}} + 155925 x^{\frac{27}{2}} + 415800 x^{\frac{25}{2}} + 727650 x^{\frac{23}{2}} + 873180 x^{\frac{21}{2}} + 727650 x^{\frac{19}{2}} + 415800 x^{\frac{17}{2}} + 155925 x^{\frac{15}{2}} + 34650 x^{\frac{13}{2}} + 3465 x^{\frac{11}{2}}} - \frac{20672 x^{13} \sqrt{x + 1}}{3465 x^{\frac{31}{2}} + 34650 x^{\frac{29}{2}} + 155925 x^{\frac{27}{2}} + 415800 x^{\frac{25}{2}} + 727650 x^{\frac{23}{2}} + 873180 x^{\frac{21}{2}} + 727650 x^{\frac{19}{2}} + 415800 x^{\frac{17}{2}} + 155925 x^{\frac{15}{2}} + 34650 x^{\frac{13}{2}} + 3465 x^{\frac{11}{2}}} - \frac{51680 x^{12} \sqrt{x + 1}}{3465 x^{\frac{31}{2}} + 34650 x^{\frac{29}{2}} + 155925 x^{\frac{27}{2}} + 415800 x^{\frac{25}{2}} + 727650 x^{\frac{23}{2}} + 873180 x^{\frac{21}{2}} + 727650 x^{\frac{19}{2}} + 415800 x^{\frac{17}{2}} + 155925 x^{\frac{15}{2}} + 34650 x^{\frac{13}{2}} + 3465 x^{\frac{11}{2}}} - \frac{83980 x^{11} \sqrt{x + 1}}{3465 x^{\frac{31}{2}} + 34650 x^{\frac{29}{2}} + 155925 x^{\frac{27}{2}} + 415800 x^{\frac{25}{2}} + 727650 x^{\frac{23}{2}} + 873180 x^{\frac{21}{2}} + 727650 x^{\frac{19}{2}} + 415800 x^{\frac{17}{2}} + 155925 x^{\frac{15}{2}} + 34650 x^{\frac{13}{2}} + 3465 x^{\frac{11}{2}}} - \frac{93764 x^{10} \sqrt{x + 1}}{3465 x^{\frac{31}{2}} + 34650 x^{\frac{29}{2}} + 155925 x^{\frac{27}{2}} + 415800 x^{\frac{25}{2}} + 727650 x^{\frac{23}{2}} + 873180 x^{\frac{21}{2}} + 727650 x^{\frac{19}{2}} + 415800 x^{\frac{17}{2}} + 155925 x^{\frac{15}{2}} + 34650 x^{\frac{13}{2}} + 3465 x^{\frac{11}{2}}} + \frac{384 x^{10} \sqrt{x + 1}}{315 x^{\frac{21}{2}} + 1890 x^{\frac{19}{2}} + 4725 x^{\frac{17}{2}} + 6300 x^{\frac{15}{2}} + 4725 x^{\frac{13}{2}} + 1890 x^{\frac{11}{2}} + 315 x^{\frac{9}{2}}} - \frac{83028 x^{9} \sqrt{x + 1}}{3465 x^{\frac{31}{2}} + 34650 x^{\frac{29}{2}} + 155925 x^{\frac{27}{2}} + 415800 x^{\frac{25}{2}} + 727650 x^{\frac{23}{2}} + 873180 x^{\frac{21}{2}} + 727650 x^{\frac{19}{2}} + 415800 x^{\frac{17}{2}} + 155925 x^{\frac{15}{2}} + 34650 x^{\frac{13}{2}} + 3465 x^{\frac{11}{2}}} + \frac{2112 x^{9} \sqrt{x + 1}}{315 x^{\frac{21}{2}} + 1890 x^{\frac{19}{2}} + 4725 x^{\frac{17}{2}} + 6300 x^{\frac{15}{2}} + 4725 x^{\frac{13}{2}} + 1890 x^{\frac{11}{2}} + 315 x^{\frac{9}{2}}} - \frac{95964 x^{8} \sqrt{x + 1}}{3465 x^{\frac{31}{2}} + 34650 x^{\frac{29}{2}} + 155925 x^{\frac{27}{2}} + 415800 x^{\frac{25}{2}} + 727650 x^{\frac{23}{2}} + 873180 x^{\frac{21}{2}} + 727650 x^{\frac{19}{2}} + 415800 x^{\frac{17}{2}} + 155925 x^{\frac{15}{2}} + 34650 x^{\frac{13}{2}} + 3465 x^{\frac{11}{2}}} + \frac{4752 x^{8} \sqrt{x + 1}}{315 x^{\frac{21}{2}} + 1890 x^{\frac{19}{2}} + 4725 x^{\frac{17}{2}} + 6300 x^{\frac{15}{2}} + 4725 x^{\frac{13}{2}} + 1890 x^{\frac{11}{2}} + 315 x^{\frac{9}{2}}} - \frac{172920 x^{7} \sqrt{x + 1}}{3465 x^{\frac{31}{2}} + 34650 x^{\frac{29}{2}} + 155925 x^{\frac{27}{2}} + 415800 x^{\frac{25}{2}} + 727650 x^{\frac{23}{2}} + 873180 x^{\frac{21}{2}} + 727650 x^{\frac{19}{2}} + 415800 x^{\frac{17}{2}} + 155925 x^{\frac{15}{2}} + 34650 x^{\frac{13}{2}} + 3465 x^{\frac{11}{2}}} + \frac{5544 x^{7} \sqrt{x + 1}}{315 x^{\frac{21}{2}} + 1890 x^{\frac{19}{2}} + 4725 x^{\frac{17}{2}} + 6300 x^{\frac{15}{2}} + 4725 x^{\frac{13}{2}} + 1890 x^{\frac{11}{2}} + 315 x^{\frac{9}{2}}} - \frac{282920 x^{6} \sqrt{x + 1}}{3465 x^{\frac{31}{2}} + 34650 x^{\frac{29}{2}} + 155925 x^{\frac{27}{2}} + 415800 x^{\frac{25}{2}} + 727650 x^{\frac{23}{2}} + 873180 x^{\frac{21}{2}} + 727650 x^{\frac{19}{2}} + 415800 x^{\frac{17}{2}} + 155925 x^{\frac{15}{2}} + 34650 x^{\frac{13}{2}} + 3465 x^{\frac{11}{2}}} + \frac{2520 x^{6} \sqrt{x + 1}}{315 x^{\frac{21}{2}} + 1890 x^{\frac{19}{2}} + 4725 x^{\frac{17}{2}} + 6300 x^{\frac{15}{2}} + 4725 x^{\frac{13}{2}} + 1890 x^{\frac{11}{2}} + 315 x^{\frac{9}{2}}} - \frac{480 x^{6} \sqrt{x + 1}}{105 x^{\frac{13}{2}} + 315 x^{\frac{11}{2}} + 315 x^{\frac{9}{2}} + 105 x^{\frac{7}{2}}} - \frac{334312 x^{5} \sqrt{x + 1}}{3465 x^{\frac{31}{2}} + 34650 x^{\frac{29}{2}} + 155925 x^{\frac{27}{2}} + 415800 x^{\frac{25}{2}} + 727650 x^{\frac{23}{2}} + 873180 x^{\frac{21}{2}} + 727650 x^{\frac{19}{2}} + 415800 x^{\frac{17}{2}} + 155925 x^{\frac{15}{2}} + 34650 x^{\frac{13}{2}} + 3465 x^{\frac{11}{2}}} - \frac{4536 x^{5} \sqrt{x + 1}}{315 x^{\frac{21}{2}} + 1890 x^{\frac{19}{2}} + 4725 x^{\frac{17}{2}} + 6300 x^{\frac{15}{2}} + 4725 x^{\frac{13}{2}} + 1890 x^{\frac{11}{2}} + 315 x^{\frac{9}{2}}} - \frac{1200 x^{5} \sqrt{x + 1}}{105 x^{\frac{13}{2}} + 315 x^{\frac{11}{2}} + 315 x^{\frac{9}{2}} + 105 x^{\frac{7}{2}}} - \frac{275864 x^{4} \sqrt{x + 1}}{3465 x^{\frac{31}{2}} + 34650 x^{\frac{29}{2}} + 155925 x^{\frac{27}{2}} + 415800 x^{\frac{25}{2}} + 727650 x^{\frac{23}{2}} + 873180 x^{\frac{21}{2}} + 727650 x^{\frac{19}{2}} + 415800 x^{\frac{17}{2}} + 155925 x^{\frac{15}{2}} + 34650 x^{\frac{13}{2}} + 3465 x^{\frac{11}{2}}} - \frac{13608 x^{4} \sqrt{x + 1}}{315 x^{\frac{21}{2}} + 1890 x^{\frac{19}{2}} + 4725 x^{\frac{17}{2}} + 6300 x^{\frac{15}{2}} + 4725 x^{\frac{13}{2}} + 1890 x^{\frac{11}{2}} + 315 x^{\frac{9}{2}}} - \frac{900 x^{4} \sqrt{x + 1}}{105 x^{\frac{13}{2}} + 315 x^{\frac{11}{2}} + 315 x^{\frac{9}{2}} + 105 x^{\frac{7}{2}}} - \frac{156092 x^{3} \sqrt{x + 1}}{3465 x^{\frac{31}{2}} + 34650 x^{\frac{29}{2}} + 155925 x^{\frac{27}{2}} + 415800 x^{\frac{25}{2}} + 727650 x^{\frac{23}{2}} + 873180 x^{\frac{21}{2}} + 727650 x^{\frac{19}{2}} + 415800 x^{\frac{17}{2}} + 155925 x^{\frac{15}{2}} + 34650 x^{\frac{13}{2}} + 3465 x^{\frac{11}{2}}} - \frac{17928 x^{3} \sqrt{x + 1}}{315 x^{\frac{21}{2}} + 1890 x^{\frac{19}{2}} + 4725 x^{\frac{17}{2}} + 6300 x^{\frac{15}{2}} + 4725 x^{\frac{13}{2}} + 1890 x^{\frac{11}{2}} + 315 x^{\frac{9}{2}}} - \frac{1200 x^{3} \sqrt{x + 1}}{105 x^{\frac{13}{2}} + 315 x^{\frac{11}{2}} + 315 x^{\frac{9}{2}} + 105 x^{\frac{7}{2}}} + \frac{160 x^{3} \sqrt{x + 1}}{15 x^{\frac{7}{2}} + 15 x^{\frac{5}{2}}} - \frac{57940 x^{2} \sqrt{x + 1}}{3465 x^{\frac{31}{2}} + 34650 x^{\frac{29}{2}} + 155925 x^{\frac{27}{2}} + 415800 x^{\frac{25}{2}} + 727650 x^{\frac{23}{2}} + 873180 x^{\frac{21}{2}} + 727650 x^{\frac{19}{2}} + 415800 x^{\frac{17}{2}} + 155925 x^{\frac{15}{2}} + 34650 x^{\frac{13}{2}} + 3465 x^{\frac{11}{2}}} - \frac{13176 x^{2} \sqrt{x + 1}}{315 x^{\frac{21}{2}} + 1890 x^{\frac{19}{2}} + 4725 x^{\frac{17}{2}} + 6300 x^{\frac{15}{2}} + 4725 x^{\frac{13}{2}} + 1890 x^{\frac{11}{2}} + 315 x^{\frac{9}{2}}} - \frac{3000 x^{2} \sqrt{x + 1}}{105 x^{\frac{13}{2}} + 315 x^{\frac{11}{2}} + 315 x^{\frac{9}{2}} + 105 x^{\frac{7}{2}}} + \frac{80 x^{2} \sqrt{x + 1}}{15 x^{\frac{7}{2}} + 15 x^{\frac{5}{2}}} - \frac{12740 x \sqrt{x + 1}}{3465 x^{\frac{31}{2}} + 34650 x^{\frac{29}{2}} + 155925 x^{\frac{27}{2}} + 415800 x^{\frac{25}{2}} + 727650 x^{\frac{23}{2}} + 873180 x^{\frac{21}{2}} + 727650 x^{\frac{19}{2}} + 415800 x^{\frac{17}{2}} + 155925 x^{\frac{15}{2}} + 34650 x^{\frac{13}{2}} + 3465 x^{\frac{11}{2}}} - \frac{5160 x \sqrt{x + 1}}{315 x^{\frac{21}{2}} + 1890 x^{\frac{19}{2}} + 4725 x^{\frac{17}{2}} + 6300 x^{\frac{15}{2}} + 4725 x^{\frac{13}{2}} + 1890 x^{\frac{11}{2}} + 315 x^{\frac{9}{2}}} - \frac{2880 x \sqrt{x + 1}}{105 x^{\frac{13}{2}} + 315 x^{\frac{11}{2}} + 315 x^{\frac{9}{2}} + 105 x^{\frac{7}{2}}} - \frac{320 x \sqrt{x + 1}}{15 x^{\frac{7}{2}} + 15 x^{\frac{5}{2}}} - 20 \left(1 + \frac{1}{x}\right)^{\frac{3}{2}} - 24 \sqrt{1 + \frac{1}{x}} - \frac{1260 \sqrt{x + 1}}{3465 x^{\frac{31}{2}} + 34650 x^{\frac{29}{2}} + 155925 x^{\frac{27}{2}} + 415800 x^{\frac{25}{2}} + 727650 x^{\frac{23}{2}} + 873180 x^{\frac{21}{2}} + 727650 x^{\frac{19}{2}} + 415800 x^{\frac{17}{2}} + 155925 x^{\frac{15}{2}} + 34650 x^{\frac{13}{2}} + 3465 x^{\frac{11}{2}}} - \frac{840 \sqrt{x + 1}}{315 x^{\frac{21}{2}} + 1890 x^{\frac{19}{2}} + 4725 x^{\frac{17}{2}} + 6300 x^{\frac{15}{2}} + 4725 x^{\frac{13}{2}} + 1890 x^{\frac{11}{2}} + 315 x^{\frac{9}{2}}} - \frac{900 \sqrt{x + 1}}{105 x^{\frac{13}{2}} + 315 x^{\frac{11}{2}} + 315 x^{\frac{9}{2}} + 105 x^{\frac{7}{2}}} - \frac{240 \sqrt{x + 1}}{15 x^{\frac{7}{2}} + 15 x^{\frac{5}{2}}} - 12 \log{\left(\sqrt{1 + \frac{1}{x}} - 1 \right)} + 12 \log{\left(\sqrt{1 + \frac{1}{x}} + 1 \right)} + 2 \operatorname{asinh}{\left(\sqrt{x} \right)}$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.