3.24.54 \(\int \frac {(a+b \sqrt [3]{x})^{15}}{x^{11}} \, dx\) [2354]

Optimal. Leaf size=217 \[ -\frac {a^{15}}{10 x^{10}}-\frac {45 a^{14} b}{29 x^{29/3}}-\frac {45 a^{13} b^2}{4 x^{28/3}}-\frac {455 a^{12} b^3}{9 x^9}-\frac {315 a^{11} b^4}{2 x^{26/3}}-\frac {9009 a^{10} b^5}{25 x^{25/3}}-\frac {5005 a^9 b^6}{8 x^8}-\frac {19305 a^8 b^7}{23 x^{23/3}}-\frac {1755 a^7 b^8}{2 x^{22/3}}-\frac {715 a^6 b^9}{x^7}-\frac {9009 a^5 b^{10}}{20 x^{20/3}}-\frac {4095 a^4 b^{11}}{19 x^{19/3}}-\frac {455 a^3 b^{12}}{6 x^6}-\frac {315 a^2 b^{13}}{17 x^{17/3}}-\frac {45 a b^{14}}{16 x^{16/3}}-\frac {b^{15}}{5 x^5} \]

[Out]

-1/10*a^15/x^10-45/29*a^14*b/x^(29/3)-45/4*a^13*b^2/x^(28/3)-455/9*a^12*b^3/x^9-315/2*a^11*b^4/x^(26/3)-9009/2
5*a^10*b^5/x^(25/3)-5005/8*a^9*b^6/x^8-19305/23*a^8*b^7/x^(23/3)-1755/2*a^7*b^8/x^(22/3)-715*a^6*b^9/x^7-9009/
20*a^5*b^10/x^(20/3)-4095/19*a^4*b^11/x^(19/3)-455/6*a^3*b^12/x^6-315/17*a^2*b^13/x^(17/3)-45/16*a*b^14/x^(16/
3)-1/5*b^15/x^5

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Rubi [A]
time = 0.08, antiderivative size = 217, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {272, 45} \begin {gather*} -\frac {a^{15}}{10 x^{10}}-\frac {45 a^{14} b}{29 x^{29/3}}-\frac {45 a^{13} b^2}{4 x^{28/3}}-\frac {455 a^{12} b^3}{9 x^9}-\frac {315 a^{11} b^4}{2 x^{26/3}}-\frac {9009 a^{10} b^5}{25 x^{25/3}}-\frac {5005 a^9 b^6}{8 x^8}-\frac {19305 a^8 b^7}{23 x^{23/3}}-\frac {1755 a^7 b^8}{2 x^{22/3}}-\frac {715 a^6 b^9}{x^7}-\frac {9009 a^5 b^{10}}{20 x^{20/3}}-\frac {4095 a^4 b^{11}}{19 x^{19/3}}-\frac {455 a^3 b^{12}}{6 x^6}-\frac {315 a^2 b^{13}}{17 x^{17/3}}-\frac {45 a b^{14}}{16 x^{16/3}}-\frac {b^{15}}{5 x^5} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(a + b*x^(1/3))^15/x^11,x]

[Out]

-1/10*a^15/x^10 - (45*a^14*b)/(29*x^(29/3)) - (45*a^13*b^2)/(4*x^(28/3)) - (455*a^12*b^3)/(9*x^9) - (315*a^11*
b^4)/(2*x^(26/3)) - (9009*a^10*b^5)/(25*x^(25/3)) - (5005*a^9*b^6)/(8*x^8) - (19305*a^8*b^7)/(23*x^(23/3)) - (
1755*a^7*b^8)/(2*x^(22/3)) - (715*a^6*b^9)/x^7 - (9009*a^5*b^10)/(20*x^(20/3)) - (4095*a^4*b^11)/(19*x^(19/3))
- (455*a^3*b^12)/(6*x^6) - (315*a^2*b^13)/(17*x^(17/3)) - (45*a*b^14)/(16*x^(16/3)) - b^15/(5*x^5)

Rule 45

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] && NeQ[b*c - a*d, 0] && 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])

Rule 272

Int[(x_)^(m_.)*((a_) + (b_.)*(x_)^(n_))^(p_), x_Symbol] :> Dist[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]]

Rubi steps

\begin {align*} \int \frac {\left (a+b \sqrt [3]{x}\right )^{15}}{x^{11}} \, dx &=3 \text {Subst}\left (\int \frac {(a+b x)^{15}}{x^{31}} \, dx,x,\sqrt [3]{x}\right )\\ &=3 \text {Subst}\left (\int \left (\frac {a^{15}}{x^{31}}+\frac {15 a^{14} b}{x^{30}}+\frac {105 a^{13} b^2}{x^{29}}+\frac {455 a^{12} b^3}{x^{28}}+\frac {1365 a^{11} b^4}{x^{27}}+\frac {3003 a^{10} b^5}{x^{26}}+\frac {5005 a^9 b^6}{x^{25}}+\frac {6435 a^8 b^7}{x^{24}}+\frac {6435 a^7 b^8}{x^{23}}+\frac {5005 a^6 b^9}{x^{22}}+\frac {3003 a^5 b^{10}}{x^{21}}+\frac {1365 a^4 b^{11}}{x^{20}}+\frac {455 a^3 b^{12}}{x^{19}}+\frac {105 a^2 b^{13}}{x^{18}}+\frac {15 a b^{14}}{x^{17}}+\frac {b^{15}}{x^{16}}\right ) \, dx,x,\sqrt [3]{x}\right )\\ &=-\frac {a^{15}}{10 x^{10}}-\frac {45 a^{14} b}{29 x^{29/3}}-\frac {45 a^{13} b^2}{4 x^{28/3}}-\frac {455 a^{12} b^3}{9 x^9}-\frac {315 a^{11} b^4}{2 x^{26/3}}-\frac {9009 a^{10} b^5}{25 x^{25/3}}-\frac {5005 a^9 b^6}{8 x^8}-\frac {19305 a^8 b^7}{23 x^{23/3}}-\frac {1755 a^7 b^8}{2 x^{22/3}}-\frac {715 a^6 b^9}{x^7}-\frac {9009 a^5 b^{10}}{20 x^{20/3}}-\frac {4095 a^4 b^{11}}{19 x^{19/3}}-\frac {455 a^3 b^{12}}{6 x^6}-\frac {315 a^2 b^{13}}{17 x^{17/3}}-\frac {45 a b^{14}}{16 x^{16/3}}-\frac {b^{15}}{5 x^5}\\ \end {align*}

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Mathematica [A]
time = 0.09, size = 189, normalized size = 0.87 \begin {gather*} \frac {-77558760 a^{15}-1203498000 a^{14} b \sqrt [3]{x}-8725360500 a^{13} b^2 x^{2/3}-39210262000 a^{12} b^3 x-122155047000 a^{11} b^4 x^{4/3}-279490747536 a^{10} b^5 x^{5/3}-485226992250 a^9 b^6 x^2-650987766000 a^8 b^7 x^{7/3}-680578119000 a^7 b^8 x^{8/3}-554545134000 a^6 b^9 x^3-349363434420 a^5 b^{10} x^{10/3}-167159538000 a^4 b^{11} x^{11/3}-58815393000 a^3 b^{12} x^4-14371182000 a^2 b^{13} x^{13/3}-2181340125 a b^{14} x^{14/3}-155117520 b^{15} x^5}{775587600 x^{10}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(a + b*x^(1/3))^15/x^11,x]

[Out]

(-77558760*a^15 - 1203498000*a^14*b*x^(1/3) - 8725360500*a^13*b^2*x^(2/3) - 39210262000*a^12*b^3*x - 122155047
000*a^11*b^4*x^(4/3) - 279490747536*a^10*b^5*x^(5/3) - 485226992250*a^9*b^6*x^2 - 650987766000*a^8*b^7*x^(7/3)
- 680578119000*a^7*b^8*x^(8/3) - 554545134000*a^6*b^9*x^3 - 349363434420*a^5*b^10*x^(10/3) - 167159538000*a^4
*b^11*x^(11/3) - 58815393000*a^3*b^12*x^4 - 14371182000*a^2*b^13*x^(13/3) - 2181340125*a*b^14*x^(14/3) - 15511
7520*b^15*x^5)/(775587600*x^10)

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Maple [A]
time = 0.19, size = 168, normalized size = 0.77

method	result	size
derivativedivides	\(-\frac {a^{15}}{10 x^{10}}-\frac {45 a^{14} b}{29 x^{\frac {29}{3}}}-\frac {45 a^{13} b^{2}}{4 x^{\frac {28}{3}}}-\frac {455 a^{12} b^{3}}{9 x^{9}}-\frac {315 a^{11} b^{4}}{2 x^{\frac {26}{3}}}-\frac {9009 a^{10} b^{5}}{25 x^{\frac {25}{3}}}-\frac {5005 a^{9} b^{6}}{8 x^{8}}-\frac {19305 a^{8} b^{7}}{23 x^{\frac {23}{3}}}-\frac {1755 a^{7} b^{8}}{2 x^{\frac {22}{3}}}-\frac {715 a^{6} b^{9}}{x^{7}}-\frac {9009 a^{5} b^{10}}{20 x^{\frac {20}{3}}}-\frac {4095 a^{4} b^{11}}{19 x^{\frac {19}{3}}}-\frac {455 a^{3} b^{12}}{6 x^{6}}-\frac {315 a^{2} b^{13}}{17 x^{\frac {17}{3}}}-\frac {45 a \,b^{14}}{16 x^{\frac {16}{3}}}-\frac {b^{15}}{5 x^{5}}\)	\(168\)
default	\(-\frac {a^{15}}{10 x^{10}}-\frac {45 a^{14} b}{29 x^{\frac {29}{3}}}-\frac {45 a^{13} b^{2}}{4 x^{\frac {28}{3}}}-\frac {455 a^{12} b^{3}}{9 x^{9}}-\frac {315 a^{11} b^{4}}{2 x^{\frac {26}{3}}}-\frac {9009 a^{10} b^{5}}{25 x^{\frac {25}{3}}}-\frac {5005 a^{9} b^{6}}{8 x^{8}}-\frac {19305 a^{8} b^{7}}{23 x^{\frac {23}{3}}}-\frac {1755 a^{7} b^{8}}{2 x^{\frac {22}{3}}}-\frac {715 a^{6} b^{9}}{x^{7}}-\frac {9009 a^{5} b^{10}}{20 x^{\frac {20}{3}}}-\frac {4095 a^{4} b^{11}}{19 x^{\frac {19}{3}}}-\frac {455 a^{3} b^{12}}{6 x^{6}}-\frac {315 a^{2} b^{13}}{17 x^{\frac {17}{3}}}-\frac {45 a \,b^{14}}{16 x^{\frac {16}{3}}}-\frac {b^{15}}{5 x^{5}}\)	\(168\)
trager	\(\frac {\left (x -1\right ) \left (36 a^{15} x^{9}+18200 a^{12} b^{3} x^{9}+225225 a^{9} b^{6} x^{9}+257400 a^{6} b^{9} x^{9}+27300 a^{3} b^{12} x^{9}+72 b^{15} x^{9}+36 a^{15} x^{8}+18200 a^{12} b^{3} x^{8}+225225 a^{9} b^{6} x^{8}+257400 a^{6} b^{9} x^{8}+27300 a^{3} b^{12} x^{8}+72 b^{15} x^{8}+36 a^{15} x^{7}+18200 a^{12} b^{3} x^{7}+225225 a^{9} b^{6} x^{7}+257400 a^{6} b^{9} x^{7}+27300 a^{3} b^{12} x^{7}+72 b^{15} x^{7}+36 a^{15} x^{6}+18200 a^{12} b^{3} x^{6}+225225 a^{9} b^{6} x^{6}+257400 a^{6} b^{9} x^{6}+27300 a^{3} b^{12} x^{6}+72 b^{15} x^{6}+36 a^{15} x^{5}+18200 a^{12} b^{3} x^{5}+225225 a^{9} b^{6} x^{5}+257400 a^{6} b^{9} x^{5}+27300 a^{3} b^{12} x^{5}+72 b^{15} x^{5}+36 a^{15} x^{4}+18200 a^{12} b^{3} x^{4}+225225 a^{9} b^{6} x^{4}+257400 a^{6} b^{9} x^{4}+27300 a^{3} b^{12} x^{4}+36 a^{15} x^{3}+18200 a^{12} b^{3} x^{3}+225225 a^{9} b^{6} x^{3}+257400 a^{6} b^{9} x^{3}+36 a^{15} x^{2}+18200 a^{12} b^{3} x^{2}+225225 a^{9} b^{6} x^{2}+36 a^{15} x +18200 a^{12} b^{3} x +36 a^{15}\right )}{360 x^{10}}-\frac {9 \left (466900 b^{12} x^{4}[phone] a^{3} b^{9} x^{3}[phone] a^{6} b^{6} x^{2}+3968650 a^{9} b^{3} x +39100 a^{12}\right ) a^{2} b}{226780 x^{\frac {29}{3}}}-\frac {9 \left (2375 b^{12} x^{4}+182000 a^{3} b^{9} x^{3}+741000 a^{6} b^{6} x^{2}+304304 a^{9} b^{3} x +9500 a^{12}\right ) a \,b^{2}}{7600 x^{\frac {28}{3}}}\)	\(562\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((a+b*x^(1/3))^15/x^11,x,method=_RETURNVERBOSE)

[Out]

-1/10*a^15/x^10-45/29*a^14*b/x^(29/3)-45/4*a^13*b^2/x^(28/3)-455/9*a^12*b^3/x^9-315/2*a^11*b^4/x^(26/3)-9009/2
5*a^10*b^5/x^(25/3)-5005/8*a^9*b^6/x^8-19305/23*a^8*b^7/x^(23/3)-1755/2*a^7*b^8/x^(22/3)-715*a^6*b^9/x^7-9009/
20*a^5*b^10/x^(20/3)-4095/19*a^4*b^11/x^(19/3)-455/6*a^3*b^12/x^6-315/17*a^2*b^13/x^(17/3)-45/16*a*b^14/x^(16/
3)-1/5*b^15/x^5

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Maxima [A]
time = 0.31, size = 167, normalized size = 0.77 \begin {gather*} -\frac {155117520 \, b^{15} x^{5} + 2181340125 \, a b^{14} x^{\frac {14}{3}} + 14371182000 \, a^{2} b^{13} x^{\frac {13}{3}} + 58815393000 \, a^{3} b^{12} x^{4} + 167159538000 \, a^{4} b^{11} x^{\frac {11}{3}} + 349363434420 \, a^{5} b^{10} x^{\frac {10}{3}} + 554545134000 \, a^{6} b^{9} x^{3} + 680578119000 \, a^{7} b^{8} x^{\frac {8}{3}} + 650987766000 \, a^{8} b^{7} x^{\frac {7}{3}} + 485226992250 \, a^{9} b^{6} x^{2} + 279490747536 \, a^{10} b^{5} x^{\frac {5}{3}} + 122155047000 \, a^{11} b^{4} x^{\frac {4}{3}} + 39210262000 \, a^{12} b^{3} x + 8725360500 \, a^{13} b^{2} x^{\frac {2}{3}} + 1203498000 \, a^{14} b x^{\frac {1}{3}} + 77558760 \, a^{15}}{775587600 \, x^{10}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((a+b*x^(1/3))^15/x^11,x, algorithm="maxima")

[Out]

-1/775587600*(155117520*b^15*x^5 + 2181340125*a*b^14*x^(14/3) + 14371182000*a^2*b^13*x^(13/3) + 58815393000*a^
3*b^12*x^4 + 167159538000*a^4*b^11*x^(11/3) + 349363434420*a^5*b^10*x^(10/3) + 554545134000*a^6*b^9*x^3 + 6805
78119000*a^7*b^8*x^(8/3) + 650987766000*a^8*b^7*x^(7/3) + 485226992250*a^9*b^6*x^2 + 279490747536*a^10*b^5*x^(
5/3) + 122155047000*a^11*b^4*x^(4/3) + 39210262000*a^12*b^3*x + 8725360500*a^13*b^2*x^(2/3) + 1203498000*a^14*
b*x^(1/3) + 77558760*a^15)/x^10

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Fricas [A]
time = 0.39, size = 169, normalized size = 0.78 \begin {gather*} -\frac {155117520 \, b^{15} x^{5} + 58815393000 \, a^{3} b^{12} x^{4} + 554545134000 \, a^{6} b^{9} x^{3} + 485226992250 \, a^{9} b^{6} x^{2} + 39210262000 \, a^{12} b^{3} x + 77558760 \, a^{15} + 918459 \, {\left (2375 \, a b^{14} x^{4} + 182000 \, a^{4} b^{11} x^{3} + 741000 \, a^{7} b^{8} x^{2} + 304304 \, a^{10} b^{5} x + 9500 \, a^{13} b^{2}\right )} x^{\frac {2}{3}} + 30780 \, {\left (466900 \, a^{2} b^{13} x^{4} + 11350339 \, a^{5} b^{10} x^{3} + 21149700 \, a^{8} b^{7} x^{2} + 3968650 \, a^{11} b^{4} x + 39100 \, a^{14} b\right )} x^{\frac {1}{3}}}{775587600 \, x^{10}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((a+b*x^(1/3))^15/x^11,x, algorithm="fricas")

[Out]

-1/775587600*(155117520*b^15*x^5 + 58815393000*a^3*b^12*x^4 + 554545134000*a^6*b^9*x^3 + 485226992250*a^9*b^6*
x^2 + 39210262000*a^12*b^3*x + 77558760*a^15 + 918459*(2375*a*b^14*x^4 + 182000*a^4*b^11*x^3 + 741000*a^7*b^8*
x^2 + 304304*a^10*b^5*x + 9500*a^13*b^2)*x^(2/3) + 30780*(466900*a^2*b^13*x^4 + 11350339*a^5*b^10*x^3 + 211497
00*a^8*b^7*x^2 + 3968650*a^11*b^4*x + 39100*a^14*b)*x^(1/3))/x^10

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Sympy [A]
time = 2.89, size = 219, normalized size = 1.01 \begin {gather*} - \frac {a^{15}}{10 x^{10}} - \frac {45 a^{14} b}{29 x^{\frac {29}{3}}} - \frac {45 a^{13} b^{2}}{4 x^{\frac {28}{3}}} - \frac {455 a^{12} b^{3}}{9 x^{9}} - \frac {315 a^{11} b^{4}}{2 x^{\frac {26}{3}}} - \frac {9009 a^{10} b^{5}}{25 x^{\frac {25}{3}}} - \frac {5005 a^{9} b^{6}}{8 x^{8}} - \frac {19305 a^{8} b^{7}}{23 x^{\frac {23}{3}}} - \frac {1755 a^{7} b^{8}}{2 x^{\frac {22}{3}}} - \frac {715 a^{6} b^{9}}{x^{7}} - \frac {9009 a^{5} b^{10}}{20 x^{\frac {20}{3}}} - \frac {4095 a^{4} b^{11}}{19 x^{\frac {19}{3}}} - \frac {455 a^{3} b^{12}}{6 x^{6}} - \frac {315 a^{2} b^{13}}{17 x^{\frac {17}{3}}} - \frac {45 a b^{14}}{16 x^{\frac {16}{3}}} - \frac {b^{15}}{5 x^{5}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((a+b*x**(1/3))**15/x**11,x)

[Out]

-a**15/(10*x**10) - 45*a**14*b/(29*x**(29/3)) - 45*a**13*b**2/(4*x**(28/3)) - 455*a**12*b**3/(9*x**9) - 315*a*
*11*b**4/(2*x**(26/3)) - 9009*a**10*b**5/(25*x**(25/3)) - 5005*a**9*b**6/(8*x**8) - 19305*a**8*b**7/(23*x**(23
/3)) - 1755*a**7*b**8/(2*x**(22/3)) - 715*a**6*b**9/x**7 - 9009*a**5*b**10/(20*x**(20/3)) - 4095*a**4*b**11/(1
9*x**(19/3)) - 455*a**3*b**12/(6*x**6) - 315*a**2*b**13/(17*x**(17/3)) - 45*a*b**14/(16*x**(16/3)) - b**15/(5*
x**5)

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Giac [A]
time = 1.30, size = 167, normalized size = 0.77 \begin {gather*} -\frac {155117520 \, b^{15} x^{5} + 2181340125 \, a b^{14} x^{\frac {14}{3}} + 14371182000 \, a^{2} b^{13} x^{\frac {13}{3}} + 58815393000 \, a^{3} b^{12} x^{4} + 167159538000 \, a^{4} b^{11} x^{\frac {11}{3}} + 349363434420 \, a^{5} b^{10} x^{\frac {10}{3}} + 554545134000 \, a^{6} b^{9} x^{3} + 680578119000 \, a^{7} b^{8} x^{\frac {8}{3}} + 650987766000 \, a^{8} b^{7} x^{\frac {7}{3}} + 485226992250 \, a^{9} b^{6} x^{2} + 279490747536 \, a^{10} b^{5} x^{\frac {5}{3}} + 122155047000 \, a^{11} b^{4} x^{\frac {4}{3}} + 39210262000 \, a^{12} b^{3} x + 8725360500 \, a^{13} b^{2} x^{\frac {2}{3}} + 1203498000 \, a^{14} b x^{\frac {1}{3}} + 77558760 \, a^{15}}{775587600 \, x^{10}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((a+b*x^(1/3))^15/x^11,x, algorithm="giac")

[Out]

-1/775587600*(155117520*b^15*x^5 + 2181340125*a*b^14*x^(14/3) + 14371182000*a^2*b^13*x^(13/3) + 58815393000*a^
3*b^12*x^4 + 167159538000*a^4*b^11*x^(11/3) + 349363434420*a^5*b^10*x^(10/3) + 554545134000*a^6*b^9*x^3 + 6805
78119000*a^7*b^8*x^(8/3) + 650987766000*a^8*b^7*x^(7/3) + 485226992250*a^9*b^6*x^2 + 279490747536*a^10*b^5*x^(
5/3) + 122155047000*a^11*b^4*x^(4/3) + 39210262000*a^12*b^3*x + 8725360500*a^13*b^2*x^(2/3) + 1203498000*a^14*
b*x^(1/3) + 77558760*a^15)/x^10

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Mupad [B]
time = 0.19, size = 167, normalized size = 0.77 \begin {gather*} -\frac {\frac {a^{15}}{10}+\frac {b^{15}\,x^5}{5}+\frac {455\,a^{12}\,b^3\,x}{9}+\frac {45\,a^{14}\,b\,x^{1/3}}{29}+\frac {45\,a\,b^{14}\,x^{14/3}}{16}+\frac {5005\,a^9\,b^6\,x^2}{8}+715\,a^6\,b^9\,x^3+\frac {455\,a^3\,b^{12}\,x^4}{6}+\frac {45\,a^{13}\,b^2\,x^{2/3}}{4}+\frac {315\,a^{11}\,b^4\,x^{4/3}}{2}+\frac {9009\,a^{10}\,b^5\,x^{5/3}}{25}+\frac {19305\,a^8\,b^7\,x^{7/3}}{23}+\frac {1755\,a^7\,b^8\,x^{8/3}}{2}+\frac {9009\,a^5\,b^{10}\,x^{10/3}}{20}+\frac {4095\,a^4\,b^{11}\,x^{11/3}}{19}+\frac {315\,a^2\,b^{13}\,x^{13/3}}{17}}{x^{10}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((a + b*x^(1/3))^15/x^11,x)

[Out]

-(a^15/10 + (b^15*x^5)/5 + (455*a^12*b^3*x)/9 + (45*a^14*b*x^(1/3))/29 + (45*a*b^14*x^(14/3))/16 + (5005*a^9*b
^6*x^2)/8 + 715*a^6*b^9*x^3 + (455*a^3*b^12*x^4)/6 + (45*a^13*b^2*x^(2/3))/4 + (315*a^11*b^4*x^(4/3))/2 + (900
9*a^10*b^5*x^(5/3))/25 + (19305*a^8*b^7*x^(7/3))/23 + (1755*a^7*b^8*x^(8/3))/2 + (9009*a^5*b^10*x^(10/3))/20 +
(4095*a^4*b^11*x^(11/3))/19 + (315*a^2*b^13*x^(13/3))/17)/x^10

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