Integrand size = 15, antiderivative size = 211 \[ \int \frac {\left (a+b \sqrt {x}\right )^{15}}{x^{16}} \, dx=-\frac {a^{15}}{15 x^{15}}-\frac {30 a^{14} b}{29 x^{29/2}}-\frac {15 a^{13} b^2}{2 x^{14}}-\frac {910 a^{12} b^3}{27 x^{27/2}}-\frac {105 a^{11} b^4}{x^{13}}-\frac {6006 a^{10} b^5}{25 x^{25/2}}-\frac {5005 a^9 b^6}{12 x^{12}}-\frac {12870 a^8 b^7}{23 x^{23/2}}-\frac {585 a^7 b^8}{x^{11}}-\frac {1430 a^6 b^9}{3 x^{21/2}}-\frac {3003 a^5 b^{10}}{10 x^{10}}-\frac {2730 a^4 b^{11}}{19 x^{19/2}}-\frac {455 a^3 b^{12}}{9 x^9}-\frac {210 a^2 b^{13}}{17 x^{17/2}}-\frac {15 a b^{14}}{8 x^8}-\frac {2 b^{15}}{15 x^{15/2}} \] Output:
-1/15*a^15/x^15-30/29*a^14*b/x^(29/2)-15/2*a^13*b^2/x^14-910/27*a^12*b^3/x ^(27/2)-105*a^11*b^4/x^13-6006/25*a^10*b^5/x^(25/2)-5005/12*a^9*b^6/x^12-1 2870/23*a^8*b^7/x^(23/2)-585*a^7*b^8/x^11-1430/3*a^6*b^9/x^(21/2)-3003/10* a^5*b^10/x^10-2730/19*a^4*b^11/x^(19/2)-455/9*a^3*b^12/x^9-210/17*a^2*b^13 /x^(17/2)-15/8*a*b^14/x^8-2/15*b^15/x^(15/2)
Time = 0.08 (sec) , antiderivative size = 185, normalized size of antiderivative = 0.88 \[ \int \frac {\left (a+b \sqrt {x}\right )^{15}}{x^{16}} \, dx=\frac {-77558760 a^{15}-1203498000 a^{14} b \sqrt {x}-8725360500 a^{13} b^2 x-39210262000 a^{12} b^3 x^{3/2}-122155047000 a^{11} b^4 x^2-279490747536 a^{10} b^5 x^{5/2}-485226992250 a^9 b^6 x^3-650987766000 a^8 b^7 x^{7/2}-680578119000 a^7 b^8 x^4-554545134000 a^6 b^9 x^{9/2}-349363434420 a^5 b^{10} x^5-167159538000 a^4 b^{11} x^{11/2}-58815393000 a^3 b^{12} x^6-14371182000 a^2 b^{13} x^{13/2}-2181340125 a b^{14} x^7-155117520 b^{15} x^{15/2}}{1163381400 x^{15}} \] Input:
Integrate[(a + b*Sqrt[x])^15/x^16,x]
Output:
(-77558760*a^15 - 1203498000*a^14*b*Sqrt[x] - 8725360500*a^13*b^2*x - 3921 0262000*a^12*b^3*x^(3/2) - 122155047000*a^11*b^4*x^2 - 279490747536*a^10*b ^5*x^(5/2) - 485226992250*a^9*b^6*x^3 - 650987766000*a^8*b^7*x^(7/2) - 680 578119000*a^7*b^8*x^4 - 554545134000*a^6*b^9*x^(9/2) - 349363434420*a^5*b^ 10*x^5 - 167159538000*a^4*b^11*x^(11/2) - 58815393000*a^3*b^12*x^6 - 14371 182000*a^2*b^13*x^(13/2) - 2181340125*a*b^14*x^7 - 155117520*b^15*x^(15/2) )/(1163381400*x^15)
Time = 0.57 (sec) , antiderivative size = 217, normalized size of antiderivative = 1.03, number of steps used = 4, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {798, 53, 2009}
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {\left (a+b \sqrt {x}\right )^{15}}{x^{16}} \, dx\) |
| \(\Big \downarrow \) 798 |
| \(\displaystyle 2 \int \frac {\left (a+b \sqrt {x}\right )^{15}}{x^{31/2}}d\sqrt {x}\) |
| \(\Big \downarrow \) 53 |
| \(\displaystyle 2 \int \left (\frac {a^{15}}{x^{31/2}}+\frac {15 b a^{14}}{x^{15}}+\frac {105 b^2 a^{13}}{x^{29/2}}+\frac {455 b^3 a^{12}}{x^{14}}+\frac {1365 b^4 a^{11}}{x^{27/2}}+\frac {3003 b^5 a^{10}}{x^{13}}+\frac {5005 b^6 a^9}{x^{25/2}}+\frac {6435 b^7 a^8}{x^{12}}+\frac {6435 b^8 a^7}{x^{23/2}}+\frac {5005 b^9 a^6}{x^{11}}+\frac {3003 b^{10} a^5}{x^{21/2}}+\frac {1365 b^{11} a^4}{x^{10}}+\frac {455 b^{12} a^3}{x^{19/2}}+\frac {105 b^{13} a^2}{x^9}+\frac {15 b^{14} a}{x^{17/2}}+\frac {b^{15}}{x^8}\right )d\sqrt {x}\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 2 \left (-\frac {a^{15}}{30 x^{15}}-\frac {15 a^{14} b}{29 x^{29/2}}-\frac {15 a^{13} b^2}{4 x^{14}}-\frac {455 a^{12} b^3}{27 x^{27/2}}-\frac {105 a^{11} b^4}{2 x^{13}}-\frac {3003 a^{10} b^5}{25 x^{25/2}}-\frac {5005 a^9 b^6}{24 x^{12}}-\frac {6435 a^8 b^7}{23 x^{23/2}}-\frac {585 a^7 b^8}{2 x^{11}}-\frac {715 a^6 b^9}{3 x^{21/2}}-\frac {3003 a^5 b^{10}}{20 x^{10}}-\frac {1365 a^4 b^{11}}{19 x^{19/2}}-\frac {455 a^3 b^{12}}{18 x^9}-\frac {105 a^2 b^{13}}{17 x^{17/2}}-\frac {15 a b^{14}}{16 x^8}-\frac {b^{15}}{15 x^{15/2}}\right )\) |
Input:
Int[(a + b*Sqrt[x])^15/x^16,x]
Output:
2*(-1/30*a^15/x^15 - (15*a^14*b)/(29*x^(29/2)) - (15*a^13*b^2)/(4*x^14) - (455*a^12*b^3)/(27*x^(27/2)) - (105*a^11*b^4)/(2*x^13) - (3003*a^10*b^5)/( 25*x^(25/2)) - (5005*a^9*b^6)/(24*x^12) - (6435*a^8*b^7)/(23*x^(23/2)) - ( 585*a^7*b^8)/(2*x^11) - (715*a^6*b^9)/(3*x^(21/2)) - (3003*a^5*b^10)/(20*x ^10) - (1365*a^4*b^11)/(19*x^(19/2)) - (455*a^3*b^12)/(18*x^9) - (105*a^2* b^13)/(17*x^(17/2)) - (15*a*b^14)/(16*x^8) - b^15/(15*x^(15/2)))
Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int [ExpandIntegrand[(a + b*x)^m*(c + d*x)^n, x], x] /; FreeQ[{a, b, c, d, n}, x] && IGtQ[m, 0] && ( !IntegerQ[n] || (EqQ[c, 0] && LeQ[7*m + 4*n + 4, 0]) || LtQ[9*m + 5*(n + 1), 0] || GtQ[m + n + 2, 0])
Int[(x_)^(m_.)*((a_) + (b_.)*(x_)^(n_))^(p_), x_Symbol] :> Simp[1/n Subst [Int[x^(Simplify[(m + 1)/n] - 1)*(a + b*x)^p, x], x, x^n], x] /; FreeQ[{a, b, m, n, p}, x] && IntegerQ[Simplify[(m + 1)/n]]
Time = 23.72 (sec) , antiderivative size = 168, normalized size of antiderivative = 0.80
| method | result | size |
| derivativedivides | \(-\frac {a^{15}}{15 x^{15}}-\frac {30 a^{14} b}{29 x^{\frac {29}{2}}}-\frac {15 a^{13} b^{2}}{2 x^{14}}-\frac {910 a^{12} b^{3}}{27 x^{\frac {27}{2}}}-\frac {105 a^{11} b^{4}}{x^{13}}-\frac {6006 a^{10} b^{5}}{25 x^{\frac {25}{2}}}-\frac {5005 a^{9} b^{6}}{12 x^{12}}-\frac {12870 a^{8} b^{7}}{23 x^{\frac {23}{2}}}-\frac {585 a^{7} b^{8}}{x^{11}}-\frac {1430 a^{6} b^{9}}{3 x^{\frac {21}{2}}}-\frac {3003 a^{5} b^{10}}{10 x^{10}}-\frac {2730 a^{4} b^{11}}{19 x^{\frac {19}{2}}}-\frac {455 a^{3} b^{12}}{9 x^{9}}-\frac {210 a^{2} b^{13}}{17 x^{\frac {17}{2}}}-\frac {15 a \,b^{14}}{8 x^{8}}-\frac {2 b^{15}}{15 x^{\frac {15}{2}}}\) | \(168\) |
| default | \(-\frac {a^{15}}{15 x^{15}}-\frac {30 a^{14} b}{29 x^{\frac {29}{2}}}-\frac {15 a^{13} b^{2}}{2 x^{14}}-\frac {910 a^{12} b^{3}}{27 x^{\frac {27}{2}}}-\frac {105 a^{11} b^{4}}{x^{13}}-\frac {6006 a^{10} b^{5}}{25 x^{\frac {25}{2}}}-\frac {5005 a^{9} b^{6}}{12 x^{12}}-\frac {12870 a^{8} b^{7}}{23 x^{\frac {23}{2}}}-\frac {585 a^{7} b^{8}}{x^{11}}-\frac {1430 a^{6} b^{9}}{3 x^{\frac {21}{2}}}-\frac {3003 a^{5} b^{10}}{10 x^{10}}-\frac {2730 a^{4} b^{11}}{19 x^{\frac {19}{2}}}-\frac {455 a^{3} b^{12}}{9 x^{9}}-\frac {210 a^{2} b^{13}}{17 x^{\frac {17}{2}}}-\frac {15 a \,b^{14}}{8 x^{8}}-\frac {2 b^{15}}{15 x^{\frac {15}{2}}}\) | \(168\) |
| orering | \(-\frac {\left (4798948275 b^{28} x^{14}-59846658375 a^{2} b^{26} x^{13}+354823433055 a^{4} b^{24} x^{12}-1316246744475 a^{6} b^{22} x^{11}+3398132958675 a^{8} b^{20} x^{10}-6440058008055 a^{10} b^{18} x^{9}+9220966476975 a^{12} b^{16} x^{8}-10118348682299 a^{14} b^{14} x^{7}+8541540497490 a^{16} b^{12} x^{6}-5515484926770 a^{18} b^{10} x^{5}+2680002218270 a^{20} b^{8} x^{4}-949745146350 a^{22} b^{6} x^{3}+231952309092 a^{24} b^{4} x^{2}-34933386700 a^{26} b^{2} x +2447112600 a^{28}\right ) \left (a +b \sqrt {x}\right )^{15}}{17450721000 x^{15} \left (-b^{2} x +a^{2}\right )^{14}}-\frac {\left (145422675 b^{28} x^{14}-1709904525 a^{2} b^{26} x^{13}+9589822515 a^{4} b^{24} x^{12}-33749916525 a^{6} b^{22} x^{11}+82881291675 a^{8} b^{20} x^{10}-149768790885 a^{10} b^{18} x^{9}+204910366155 a^{12} b^{16} x^{8}-215284014517 a^{14} b^{14} x^{7}+174317153010 a^{16} b^{12} x^{6}-108146763270 a^{18} b^{10} x^{5}+50566079590 a^{20} b^{8} x^{4}-17268093570 a^{22} b^{6} x^{3}+4069338756 a^{24} b^{4} x^{2}-592091300 a^{26} b^{2} x +40116600 a^{28}\right ) x^{2} \left (\frac {15 \left (a +b \sqrt {x}\right )^{14} b}{2 x^{\frac {33}{2}}}-\frac {16 \left (a +b \sqrt {x}\right )^{15}}{x^{17}}\right )}{8725360500 \left (-b^{2} x +a^{2}\right )^{14}}\) | \(385\) |
| trager | \(\text {Expression too large to display}\) | \(1032\) |
Input:
int((a+b*x^(1/2))^15/x^16,x,method=_RETURNVERBOSE)
Output:
-1/15*a^15/x^15-30/29*a^14*b/x^(29/2)-15/2*a^13*b^2/x^14-910/27*a^12*b^3/x ^(27/2)-105*a^11*b^4/x^13-6006/25*a^10*b^5/x^(25/2)-5005/12*a^9*b^6/x^12-1 2870/23*a^8*b^7/x^(23/2)-585*a^7*b^8/x^11-1430/3*a^6*b^9/x^(21/2)-3003/10* a^5*b^10/x^10-2730/19*a^4*b^11/x^(19/2)-455/9*a^3*b^12/x^9-210/17*a^2*b^13 /x^(17/2)-15/8*a*b^14/x^8-2/15*b^15/x^(15/2)
Time = 0.07 (sec) , antiderivative size = 168, normalized size of antiderivative = 0.80 \[ \int \frac {\left (a+b \sqrt {x}\right )^{15}}{x^{16}} \, dx=-\frac {2181340125 \, a b^{14} x^{7} + 58815393000 \, a^{3} b^{12} x^{6} + 349363434420 \, a^{5} b^{10} x^{5} + 680578119000 \, a^{7} b^{8} x^{4} + 485226992250 \, a^{9} b^{6} x^{3} + 122155047000 \, a^{11} b^{4} x^{2} + 8725360500 \, a^{13} b^{2} x + 77558760 \, a^{15} + 16 \, {\left (9694845 \, b^{15} x^{7} + 898198875 \, a^{2} b^{13} x^{6} + 10447471125 \, a^{4} b^{11} x^{5} + 34659070875 \, a^{6} b^{9} x^{4} + 40686735375 \, a^{8} b^{7} x^{3} + 17468171721 \, a^{10} b^{5} x^{2} + 2450641375 \, a^{12} b^{3} x + 75218625 \, a^{14} b\right )} \sqrt {x}}{1163381400 \, x^{15}} \] Input:
integrate((a+b*x^(1/2))^15/x^16,x, algorithm="fricas")
Output:
-1/1163381400*(2181340125*a*b^14*x^7 + 58815393000*a^3*b^12*x^6 + 34936343 4420*a^5*b^10*x^5 + 680578119000*a^7*b^8*x^4 + 485226992250*a^9*b^6*x^3 + 122155047000*a^11*b^4*x^2 + 8725360500*a^13*b^2*x + 77558760*a^15 + 16*(96 94845*b^15*x^7 + 898198875*a^2*b^13*x^6 + 10447471125*a^4*b^11*x^5 + 34659 070875*a^6*b^9*x^4 + 40686735375*a^8*b^7*x^3 + 17468171721*a^10*b^5*x^2 + 2450641375*a^12*b^3*x + 75218625*a^14*b)*sqrt(x))/x^15
Time = 2.98 (sec) , antiderivative size = 216, normalized size of antiderivative = 1.02 \[ \int \frac {\left (a+b \sqrt {x}\right )^{15}}{x^{16}} \, dx=- \frac {a^{15}}{15 x^{15}} - \frac {30 a^{14} b}{29 x^{\frac {29}{2}}} - \frac {15 a^{13} b^{2}}{2 x^{14}} - \frac {910 a^{12} b^{3}}{27 x^{\frac {27}{2}}} - \frac {105 a^{11} b^{4}}{x^{13}} - \frac {6006 a^{10} b^{5}}{25 x^{\frac {25}{2}}} - \frac {5005 a^{9} b^{6}}{12 x^{12}} - \frac {12870 a^{8} b^{7}}{23 x^{\frac {23}{2}}} - \frac {585 a^{7} b^{8}}{x^{11}} - \frac {1430 a^{6} b^{9}}{3 x^{\frac {21}{2}}} - \frac {3003 a^{5} b^{10}}{10 x^{10}} - \frac {2730 a^{4} b^{11}}{19 x^{\frac {19}{2}}} - \frac {455 a^{3} b^{12}}{9 x^{9}} - \frac {210 a^{2} b^{13}}{17 x^{\frac {17}{2}}} - \frac {15 a b^{14}}{8 x^{8}} - \frac {2 b^{15}}{15 x^{\frac {15}{2}}} \] Input:
integrate((a+b*x**(1/2))**15/x**16,x)
Output:
-a**15/(15*x**15) - 30*a**14*b/(29*x**(29/2)) - 15*a**13*b**2/(2*x**14) - 910*a**12*b**3/(27*x**(27/2)) - 105*a**11*b**4/x**13 - 6006*a**10*b**5/(25 *x**(25/2)) - 5005*a**9*b**6/(12*x**12) - 12870*a**8*b**7/(23*x**(23/2)) - 585*a**7*b**8/x**11 - 1430*a**6*b**9/(3*x**(21/2)) - 3003*a**5*b**10/(10* x**10) - 2730*a**4*b**11/(19*x**(19/2)) - 455*a**3*b**12/(9*x**9) - 210*a* *2*b**13/(17*x**(17/2)) - 15*a*b**14/(8*x**8) - 2*b**15/(15*x**(15/2))
Time = 0.03 (sec) , antiderivative size = 167, normalized size of antiderivative = 0.79 \[ \int \frac {\left (a+b \sqrt {x}\right )^{15}}{x^{16}} \, dx=-\frac {155117520 \, b^{15} x^{\frac {15}{2}} + 2181340125 \, a b^{14} x^{7} + 14371182000 \, a^{2} b^{13} x^{\frac {13}{2}} + 58815393000 \, a^{3} b^{12} x^{6} + 167159538000 \, a^{4} b^{11} x^{\frac {11}{2}} + 349363434420 \, a^{5} b^{10} x^{5} + 554545134000 \, a^{6} b^{9} x^{\frac {9}{2}} + 680578119000 \, a^{7} b^{8} x^{4} + 650987766000 \, a^{8} b^{7} x^{\frac {7}{2}} + 485226992250 \, a^{9} b^{6} x^{3} + 279490747536 \, a^{10} b^{5} x^{\frac {5}{2}} + 122155047000 \, a^{11} b^{4} x^{2} + 39210262000 \, a^{12} b^{3} x^{\frac {3}{2}} + 8725360500 \, a^{13} b^{2} x + 1203498000 \, a^{14} b \sqrt {x} + 77558760 \, a^{15}}{1163381400 \, x^{15}} \] Input:
integrate((a+b*x^(1/2))^15/x^16,x, algorithm="maxima")
Output:
-1/1163381400*(155117520*b^15*x^(15/2) + 2181340125*a*b^14*x^7 + 143711820 00*a^2*b^13*x^(13/2) + 58815393000*a^3*b^12*x^6 + 167159538000*a^4*b^11*x^ (11/2) + 349363434420*a^5*b^10*x^5 + 554545134000*a^6*b^9*x^(9/2) + 680578 119000*a^7*b^8*x^4 + 650987766000*a^8*b^7*x^(7/2) + 485226992250*a^9*b^6*x ^3 + 279490747536*a^10*b^5*x^(5/2) + 122155047000*a^11*b^4*x^2 + 392102620 00*a^12*b^3*x^(3/2) + 8725360500*a^13*b^2*x + 1203498000*a^14*b*sqrt(x) + 77558760*a^15)/x^15
Time = 0.13 (sec) , antiderivative size = 167, normalized size of antiderivative = 0.79 \[ \int \frac {\left (a+b \sqrt {x}\right )^{15}}{x^{16}} \, dx=-\frac {155117520 \, b^{15} x^{\frac {15}{2}} + 2181340125 \, a b^{14} x^{7} + 14371182000 \, a^{2} b^{13} x^{\frac {13}{2}} + 58815393000 \, a^{3} b^{12} x^{6} + 167159538000 \, a^{4} b^{11} x^{\frac {11}{2}} + 349363434420 \, a^{5} b^{10} x^{5} + 554545134000 \, a^{6} b^{9} x^{\frac {9}{2}} + 680578119000 \, a^{7} b^{8} x^{4} + 650987766000 \, a^{8} b^{7} x^{\frac {7}{2}} + 485226992250 \, a^{9} b^{6} x^{3} + 279490747536 \, a^{10} b^{5} x^{\frac {5}{2}} + 122155047000 \, a^{11} b^{4} x^{2} + 39210262000 \, a^{12} b^{3} x^{\frac {3}{2}} + 8725360500 \, a^{13} b^{2} x + 1203498000 \, a^{14} b \sqrt {x} + 77558760 \, a^{15}}{1163381400 \, x^{15}} \] Input:
integrate((a+b*x^(1/2))^15/x^16,x, algorithm="giac")
Output:
-1/1163381400*(155117520*b^15*x^(15/2) + 2181340125*a*b^14*x^7 + 143711820 00*a^2*b^13*x^(13/2) + 58815393000*a^3*b^12*x^6 + 167159538000*a^4*b^11*x^ (11/2) + 349363434420*a^5*b^10*x^5 + 554545134000*a^6*b^9*x^(9/2) + 680578 119000*a^7*b^8*x^4 + 650987766000*a^8*b^7*x^(7/2) + 485226992250*a^9*b^6*x ^3 + 279490747536*a^10*b^5*x^(5/2) + 122155047000*a^11*b^4*x^2 + 392102620 00*a^12*b^3*x^(3/2) + 8725360500*a^13*b^2*x + 1203498000*a^14*b*sqrt(x) + 77558760*a^15)/x^15
Time = 0.49 (sec) , antiderivative size = 167, normalized size of antiderivative = 0.79 \[ \int \frac {\left (a+b \sqrt {x}\right )^{15}}{x^{16}} \, dx=-\frac {\frac {a^{15}}{15}+\frac {2\,b^{15}\,x^{15/2}}{15}+\frac {15\,a^{13}\,b^2\,x}{2}+\frac {30\,a^{14}\,b\,\sqrt {x}}{29}+\frac {15\,a\,b^{14}\,x^7}{8}+105\,a^{11}\,b^4\,x^2+\frac {5005\,a^9\,b^6\,x^3}{12}+585\,a^7\,b^8\,x^4+\frac {3003\,a^5\,b^{10}\,x^5}{10}+\frac {910\,a^{12}\,b^3\,x^{3/2}}{27}+\frac {455\,a^3\,b^{12}\,x^6}{9}+\frac {6006\,a^{10}\,b^5\,x^{5/2}}{25}+\frac {12870\,a^8\,b^7\,x^{7/2}}{23}+\frac {1430\,a^6\,b^9\,x^{9/2}}{3}+\frac {2730\,a^4\,b^{11}\,x^{11/2}}{19}+\frac {210\,a^2\,b^{13}\,x^{13/2}}{17}}{x^{15}} \] Input:
int((a + b*x^(1/2))^15/x^16,x)
Output:
-(a^15/15 + (2*b^15*x^(15/2))/15 + (15*a^13*b^2*x)/2 + (30*a^14*b*x^(1/2)) /29 + (15*a*b^14*x^7)/8 + 105*a^11*b^4*x^2 + (5005*a^9*b^6*x^3)/12 + 585*a ^7*b^8*x^4 + (3003*a^5*b^10*x^5)/10 + (910*a^12*b^3*x^(3/2))/27 + (455*a^3 *b^12*x^6)/9 + (6006*a^10*b^5*x^(5/2))/25 + (12870*a^8*b^7*x^(7/2))/23 + ( 1430*a^6*b^9*x^(9/2))/3 + (2730*a^4*b^11*x^(11/2))/19 + (210*a^2*b^13*x^(1 3/2))/17)/x^15
Time = 0.21 (sec) , antiderivative size = 185, normalized size of antiderivative = 0.88 \[ \int \frac {\left (a+b \sqrt {x}\right )^{15}}{x^{16}} \, dx=\frac {-77558760 \sqrt {x}\, a^{15}-8725360500 \sqrt {x}\, a^{13} b^{2} x -122155047000 \sqrt {x}\, a^{11} b^{4} x^{2}-485226992250 \sqrt {x}\, a^{9} b^{6} x^{3}-680578119000 \sqrt {x}\, a^{7} b^{8} x^{4}-349363434420 \sqrt {x}\, a^{5} b^{10} x^{5}-58815393000 \sqrt {x}\, a^{3} b^{12} x^{6}-2181340125 \sqrt {x}\, a \,b^{14} x^{7}-1203498000 a^{14} b x -39210262000 a^{12} b^{3} x^{2}-279490747536 a^{10} b^{5} x^{3}-650987766000 a^{8} b^{7} x^{4}-554545134000 a^{6} b^{9} x^{5}-167159538000 a^{4} b^{11} x^{6}-14371182000 a^{2} b^{13} x^{7}-155117520 b^{15} x^{8}}{1163381400 \sqrt {x}\, x^{15}} \] Input:
int((a+b*x^(1/2))^15/x^16,x)
Output:
( - 77558760*sqrt(x)*a**15 - 8725360500*sqrt(x)*a**13*b**2*x - 12215504700 0*sqrt(x)*a**11*b**4*x**2 - 485226992250*sqrt(x)*a**9*b**6*x**3 - 68057811 9000*sqrt(x)*a**7*b**8*x**4 - 349363434420*sqrt(x)*a**5*b**10*x**5 - 58815 393000*sqrt(x)*a**3*b**12*x**6 - 2181340125*sqrt(x)*a*b**14*x**7 - 1203498 000*a**14*b*x - 39210262000*a**12*b**3*x**2 - 279490747536*a**10*b**5*x**3 - 650987766000*a**8*b**7*x**4 - 554545134000*a**6*b**9*x**5 - 16715953800 0*a**4*b**11*x**6 - 14371182000*a**2*b**13*x**7 - 155117520*b**15*x**8)/(1 163381400*sqrt(x)*x**15)