3.1.99 \(\int x^2 (b+2 c x^3) (-a+b x^3+c x^6)^{13} \, dx\) [99]

Optimal. Leaf size=20 \[ \frac {1}{42} \left (a-b x^3-c x^6\right )^{14} \]

[Out]

1/42*(-c*x^6-b*x^3+a)^14

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Rubi [A]
time = 0.20, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {1482, 643} \begin {gather*} \frac {1}{42} \left (a-b x^3-c x^6\right )^{14} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[x^2*(b + 2*c*x^3)*(-a + b*x^3 + c*x^6)^13,x]

[Out]

(a - b*x^3 - c*x^6)^14/42

Rule 643

Int[((d_) + (e_.)*(x_))*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :> Simp[d*((a + b*x + c*x^2)^(p +
1)/(b*(p + 1))), x] /; FreeQ[{a, b, c, d, e, p}, x] && EqQ[2*c*d - b*e, 0] && NeQ[p, -1]

Rule 1482

Int[(x_)^(m_.)*((a_) + (c_.)*(x_)^(n2_.) + (b_.)*(x_)^(n_))^(p_.)*((d_) + (e_.)*(x_)^(n_))^(q_.), x_Symbol] :>
Dist[1/n, Subst[Int[(d + e*x)^q*(a + b*x + c*x^2)^p, x], x, x^n], x] /; FreeQ[{a, b, c, d, e, m, n, p, q}, x]
&& EqQ[n2, 2*n] && EqQ[Simplify[m - n + 1], 0]

Rubi steps

\begin {align*} \int x^2 \left (b+2 c x^3\right ) \left (-a+b x^3+c x^6\right )^{13} \, dx &=\frac {1}{3} \text {Subst}\left (\int (b+2 c x) \left (-a+b x+c x^2\right )^{13} \, dx,x,x^3\right )\\ &=\frac {1}{42} \left (a-b x^3-c x^6\right )^{14}\\ \end {align*}

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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(233\) vs. \(2(20)=40\).
time = 0.12, size = 233, normalized size = 11.65 \begin {gather*} \frac {1}{42} x^3 \left (b+c x^3\right ) \left (-14 a^{13}+91 a^{12} x^3 \left (b+c x^3\right )-364 a^{11} x^6 \left (b+c x^3\right )^2+1001 a^{10} x^9 \left (b+c x^3\right )^3-2002 a^9 x^{12} \left (b+c x^3\right )^4+3003 a^8 x^{15} \left (b+c x^3\right )^5-3432 a^7 x^{18} \left (b+c x^3\right )^6+3003 a^6 x^{21} \left (b+c x^3\right )^7-2002 a^5 x^{24} \left (b+c x^3\right )^8+1001 a^4 x^{27} \left (b+c x^3\right )^9-364 a^3 x^{30} \left (b+c x^3\right )^{10}+91 a^2 x^{33} \left (b+c x^3\right )^{11}-14 a x^{36} \left (b+c x^3\right )^{12}+x^{39} \left (b+c x^3\right )^{13}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[x^2*(b + 2*c*x^3)*(-a + b*x^3 + c*x^6)^13,x]

[Out]

(x^3*(b + c*x^3)*(-14*a^13 + 91*a^12*x^3*(b + c*x^3) - 364*a^11*x^6*(b + c*x^3)^2 + 1001*a^10*x^9*(b + c*x^3)^
3 - 2002*a^9*x^12*(b + c*x^3)^4 + 3003*a^8*x^15*(b + c*x^3)^5 - 3432*a^7*x^18*(b + c*x^3)^6 + 3003*a^6*x^21*(b
+ c*x^3)^7 - 2002*a^5*x^24*(b + c*x^3)^8 + 1001*a^4*x^27*(b + c*x^3)^9 - 364*a^3*x^30*(b + c*x^3)^10 + 91*a^2
*x^33*(b + c*x^3)^11 - 14*a*x^36*(b + c*x^3)^12 + x^39*(b + c*x^3)^13))/42

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Maple [A]
time = 0.09, size = 19, normalized size = 0.95

method	result	size
default	\(\frac {\left (c \,x^{6}+b \,x^{3}-a \right )^{14}}{42}\)	\(19\)
gosper	\(-\frac {x^{3} \left (-c^{14} x^{81}-14 b \,c^{13} x^{78}+14 x^{75} a \,c^{13}-91 x^{75} b^{2} c^{12}+182 x^{72} a b \,c^{12}-364 x^{72} b^{3} c^{11}-91 x^{69} a^{2} c^{12}+1092 x^{69} a \,b^{2} c^{11}-1001 x^{69} b^{4} c^{10}-1092 x^{66} a^{2} b \,c^{11}+4004 x^{66} a \,b^{3} c^{10}-2002 x^{66} b^{5} c^{9}+364 x^{63} a^{3} c^{11}-6006 x^{63} a^{2} b^{2} c^{10}+10010 x^{63} a \,b^{4} c^{9}-3003 x^{63} b^{6} c^{8}+4004 x^{60} a^{3} b \,c^{10}-20020 x^{60} a^{2} b^{3} c^{9}+18018 x^{60} a \,b^{5} c^{8}-3432 x^{60} b^{7} c^{7}-1001 x^{57} a^{4} c^{10}+20020 x^{57} a^{3} b^{2} c^{9}-45045 x^{57} a^{2} b^{4} c^{8}+24024 x^{57} a \,b^{6} c^{7}-3003 x^{57} b^{8} c^{6}-10010 x^{54} a^{4} b \,c^{9}+60060 x^{54} a^{3} b^{3} c^{8}-72072 x^{54} a^{2} b^{5} c^{7}+24024 x^{54} a \,b^{7} c^{6}-2002 x^{54} b^{9} c^{5}+2002 x^{51} a^{5} c^{9}-45045 x^{51} a^{4} b^{2} c^{8}+120120 x^{51} a^{3} b^{4} c^{7}-84084 x^{51} a^{2} b^{6} c^{6}+18018 x^{51} a \,b^{8} c^{5}-1001 x^{51} b^{10} c^{4}+18018 x^{48} a^{5} b \,c^{8}-120120 x^{48} a^{4} b^{3} c^{7}+168168 x^{48} a^{3} b^{5} c^{6}-72072 x^{48} a^{2} b^{7} c^{5}+10010 x^{48} a \,b^{9} c^{4}-364 x^{48} b^{11} c^{3}-3003 x^{45} a^{6} c^{8}+72072 x^{45} a^{5} b^{2} c^{7}-210210 x^{45} a^{4} b^{4} c^{6}+168168 x^{45} a^{3} b^{6} c^{5}-45045 x^{45} a^{2} b^{8} c^{4}+4004 x^{45} a \,b^{10} c^{3}-91 x^{45} b^{12} c^{2}-24024 x^{42} a^{6} b \,c^{7}+168168 x^{42} a^{5} b^{3} c^{6}-252252 x^{42} a^{4} b^{5} c^{5}+120120 x^{42} a^{3} b^{7} c^{4}-20020 x^{42} a^{2} b^{9} c^{3}+1092 x^{42} a \,b^{11} c^{2}-14 x^{42} b^{13} c +3432 x^{39} a^{7} c^{7}-84084 x^{39} a^{6} b^{2} c^{6}+252252 x^{39} a^{5} b^{4} c^{5}-210210 x^{39} a^{4} b^{6} c^{4}+60060 x^{39} a^{3} b^{8} c^{3}-6006 x^{39} a^{2} b^{10} c^{2}+182 x^{39} a \,b^{12} c -x^{39} b^{14}+24024 x^{36} a^{7} b \,c^{6}-168168 x^{36} a^{6} b^{3} c^{5}+252252 x^{36} a^{5} b^{5} c^{4}-120120 x^{36} a^{4} b^{7} c^{3}+20020 x^{36} a^{3} b^{9} c^{2}-1092 x^{36} a^{2} b^{11} c +14 x^{36} a \,b^{13}-3003 x^{33} a^{8} c^{6}+72072 x^{33} a^{7} b^{2} c^{5}-210210 x^{33} a^{6} b^{4} c^{4}+168168 x^{33} a^{5} b^{6} c^{3}-45045 x^{33} a^{4} b^{8} c^{2}+4004 x^{33} a^{3} b^{10} c -91 x^{33} a^{2} b^{12}-18018 x^{30} a^{8} b \,c^{5}+120120 x^{30} a^{7} b^{3} c^{4}-168168 x^{30} a^{6} b^{5} c^{3}+72072 x^{30} a^{5} b^{7} c^{2}-10010 x^{30} a^{4} b^{9} c +364 x^{30} a^{3} b^{11}+2002 x^{27} a^{9} c^{5}-45045 x^{27} a^{8} b^{2} c^{4}+120120 x^{27} a^{7} b^{4} c^{3}-84084 x^{27} a^{6} b^{6} c^{2}+18018 x^{27} a^{5} b^{8} c -1001 x^{27} a^{4} b^{10}+10010 x^{24} a^{9} b \,c^{4}-60060 x^{24} a^{8} b^{3} c^{3}+72072 x^{24} a^{7} b^{5} c^{2}-24024 x^{24} a^{6} b^{7} c +2002 x^{24} a^{5} b^{9}-1001 x^{21} a^{10} c^{4}+20020 x^{21} a^{9} b^{2} c^{3}-45045 x^{21} a^{8} b^{4} c^{2}+24024 x^{21} a^{7} b^{6} c -3003 x^{21} a^{6} b^{8}-4004 x^{18} a^{10} b \,c^{3}+20020 x^{18} a^{9} b^{3} c^{2}-18018 x^{18} a^{8} b^{5} c +3432 x^{18} a^{7} b^{7}+364 x^{15} a^{11} c^{3}-6006 x^{15} a^{10} b^{2} c^{2}+10010 x^{15} a^{9} b^{4} c -3003 x^{15} a^{8} b^{6}+1092 x^{12} a^{11} b \,c^{2}-4004 x^{12} a^{10} b^{3} c +2002 x^{12} a^{9} b^{5}-91 x^{9} a^{12} c^{2}+1092 x^{9} a^{11} b^{2} c -1001 x^{9} a^{10} b^{4}-182 x^{6} c \,a^{12} b +364 x^{6} a^{11} b^{3}+14 x^{3} c \,a^{13}-91 x^{3} b^{2} a^{12}+14 b \,a^{13}\right )}{42}\)	\(1457\)
risch	\(\text {Expression too large to display}\)	\(1460\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^2*(2*c*x^3+b)*(c*x^6+b*x^3-a)^13,x,method=_RETURNVERBOSE)

[Out]

1/42*(c*x^6+b*x^3-a)^14

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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 1242 vs. \(2 (18) = 36\).
time = 0.29, size = 1242, normalized size = 62.10 \begin {gather*} \frac {1}{42} \, c^{14} x^{84} + \frac {1}{3} \, b c^{13} x^{81} + \frac {1}{6} \, {\left (13 \, b^{2} c^{12} - 2 \, a c^{13}\right )} x^{78} + \frac {13}{3} \, {\left (2 \, b^{3} c^{11} - a b c^{12}\right )} x^{75} + \frac {13}{6} \, {\left (11 \, b^{4} c^{10} - 12 \, a b^{2} c^{11} + a^{2} c^{12}\right )} x^{72} + \frac {13}{3} \, {\left (11 \, b^{5} c^{9} - 22 \, a b^{3} c^{10} + 6 \, a^{2} b c^{11}\right )} x^{69} + \frac {13}{6} \, {\left (33 \, b^{6} c^{8} - 110 \, a b^{4} c^{9} + 66 \, a^{2} b^{2} c^{10} - 4 \, a^{3} c^{11}\right )} x^{66} + \frac {143}{21} \, {\left (12 \, b^{7} c^{7} - 63 \, a b^{5} c^{8} + 70 \, a^{2} b^{3} c^{9} - 14 \, a^{3} b c^{10}\right )} x^{63} + \frac {143}{6} \, {\left (3 \, b^{8} c^{6} - 24 \, a b^{6} c^{7} + 45 \, a^{2} b^{4} c^{8} - 20 \, a^{3} b^{2} c^{9} + a^{4} c^{10}\right )} x^{60} + \frac {143}{3} \, {\left (b^{9} c^{5} - 12 \, a b^{7} c^{6} + 36 \, a^{2} b^{5} c^{7} - 30 \, a^{3} b^{3} c^{8} + 5 \, a^{4} b c^{9}\right )} x^{57} + \frac {143}{6} \, {\left (b^{10} c^{4} - 18 \, a b^{8} c^{5} + 84 \, a^{2} b^{6} c^{6} - 120 \, a^{3} b^{4} c^{7} + 45 \, a^{4} b^{2} c^{8} - 2 \, a^{5} c^{9}\right )} x^{54} + \frac {13}{3} \, {\left (2 \, b^{11} c^{3} - 55 \, a b^{9} c^{4} + 396 \, a^{2} b^{7} c^{5} - 924 \, a^{3} b^{5} c^{6} + 660 \, a^{4} b^{3} c^{7} - 99 \, a^{5} b c^{8}\right )} x^{51} + \frac {13}{6} \, {\left (b^{12} c^{2} - 44 \, a b^{10} c^{3} + 495 \, a^{2} b^{8} c^{4} - 1848 \, a^{3} b^{6} c^{5} + 2310 \, a^{4} b^{4} c^{6} - 792 \, a^{5} b^{2} c^{7} + 33 \, a^{6} c^{8}\right )} x^{48} + \frac {1}{3} \, {\left (b^{13} c - 78 \, a b^{11} c^{2} + 1430 \, a^{2} b^{9} c^{3} - 8580 \, a^{3} b^{7} c^{4} + 18018 \, a^{4} b^{5} c^{5} - 12012 \, a^{5} b^{3} c^{6} + 1716 \, a^{6} b c^{7}\right )} x^{45} + \frac {1}{42} \, {\left (b^{14} - 182 \, a b^{12} c + 6006 \, a^{2} b^{10} c^{2} - 60060 \, a^{3} b^{8} c^{3} + 210210 \, a^{4} b^{6} c^{4} - 252252 \, a^{5} b^{4} c^{5} + 84084 \, a^{6} b^{2} c^{6} - 3432 \, a^{7} c^{7}\right )} x^{42} - \frac {1}{3} \, {\left (a b^{13} - 78 \, a^{2} b^{11} c + 1430 \, a^{3} b^{9} c^{2} - 8580 \, a^{4} b^{7} c^{3} + 18018 \, a^{5} b^{5} c^{4} - 12012 \, a^{6} b^{3} c^{5} + 1716 \, a^{7} b c^{6}\right )} x^{39} + \frac {13}{6} \, {\left (a^{2} b^{12} - 44 \, a^{3} b^{10} c + 495 \, a^{4} b^{8} c^{2} - 1848 \, a^{5} b^{6} c^{3} + 2310 \, a^{6} b^{4} c^{4} - 792 \, a^{7} b^{2} c^{5} + 33 \, a^{8} c^{6}\right )} x^{36} - \frac {13}{3} \, {\left (2 \, a^{3} b^{11} - 55 \, a^{4} b^{9} c + 396 \, a^{5} b^{7} c^{2} - 924 \, a^{6} b^{5} c^{3} + 660 \, a^{7} b^{3} c^{4} - 99 \, a^{8} b c^{5}\right )} x^{33} + \frac {143}{6} \, {\left (a^{4} b^{10} - 18 \, a^{5} b^{8} c + 84 \, a^{6} b^{6} c^{2} - 120 \, a^{7} b^{4} c^{3} + 45 \, a^{8} b^{2} c^{4} - 2 \, a^{9} c^{5}\right )} x^{30} - \frac {143}{3} \, {\left (a^{5} b^{9} - 12 \, a^{6} b^{7} c + 36 \, a^{7} b^{5} c^{2} - 30 \, a^{8} b^{3} c^{3} + 5 \, a^{9} b c^{4}\right )} x^{27} + \frac {143}{6} \, {\left (3 \, a^{6} b^{8} - 24 \, a^{7} b^{6} c + 45 \, a^{8} b^{4} c^{2} - 20 \, a^{9} b^{2} c^{3} + a^{10} c^{4}\right )} x^{24} - \frac {143}{21} \, {\left (12 \, a^{7} b^{7} - 63 \, a^{8} b^{5} c + 70 \, a^{9} b^{3} c^{2} - 14 \, a^{10} b c^{3}\right )} x^{21} + \frac {13}{6} \, {\left (33 \, a^{8} b^{6} - 110 \, a^{9} b^{4} c + 66 \, a^{10} b^{2} c^{2} - 4 \, a^{11} c^{3}\right )} x^{18} - \frac {1}{3} \, a^{13} b x^{3} - \frac {13}{3} \, {\left (11 \, a^{9} b^{5} - 22 \, a^{10} b^{3} c + 6 \, a^{11} b c^{2}\right )} x^{15} + \frac {13}{6} \, {\left (11 \, a^{10} b^{4} - 12 \, a^{11} b^{2} c + a^{12} c^{2}\right )} x^{12} - \frac {13}{3} \, {\left (2 \, a^{11} b^{3} - a^{12} b c\right )} x^{9} + \frac {1}{6} \, {\left (13 \, a^{12} b^{2} - 2 \, a^{13} c\right )} x^{6} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^2*(2*c*x^3+b)*(c*x^6+b*x^3-a)^13,x, algorithm="maxima")

[Out]

1/42*c^14*x^84 + 1/3*b*c^13*x^81 + 1/6*(13*b^2*c^12 - 2*a*c^13)*x^78 + 13/3*(2*b^3*c^11 - a*b*c^12)*x^75 + 13/
6*(11*b^4*c^10 - 12*a*b^2*c^11 + a^2*c^12)*x^72 + 13/3*(11*b^5*c^9 - 22*a*b^3*c^10 + 6*a^2*b*c^11)*x^69 + 13/6
*(33*b^6*c^8 - 110*a*b^4*c^9 + 66*a^2*b^2*c^10 - 4*a^3*c^11)*x^66 + 143/21*(12*b^7*c^7 - 63*a*b^5*c^8 + 70*a^2
*b^3*c^9 - 14*a^3*b*c^10)*x^63 + 143/6*(3*b^8*c^6 - 24*a*b^6*c^7 + 45*a^2*b^4*c^8 - 20*a^3*b^2*c^9 + a^4*c^10)
*x^60 + 143/3*(b^9*c^5 - 12*a*b^7*c^6 + 36*a^2*b^5*c^7 - 30*a^3*b^3*c^8 + 5*a^4*b*c^9)*x^57 + 143/6*(b^10*c^4
- 18*a*b^8*c^5 + 84*a^2*b^6*c^6 - 120*a^3*b^4*c^7 + 45*a^4*b^2*c^8 - 2*a^5*c^9)*x^54 + 13/3*(2*b^11*c^3 - 55*a
*b^9*c^4 + 396*a^2*b^7*c^5 - 924*a^3*b^5*c^6 + 660*a^4*b^3*c^7 - 99*a^5*b*c^8)*x^51 + 13/6*(b^12*c^2 - 44*a*b^
10*c^3 + 495*a^2*b^8*c^4 - 1848*a^3*b^6*c^5 + 2310*a^4*b^4*c^6 - 792*a^5*b^2*c^7 + 33*a^6*c^8)*x^48 + 1/3*(b^1
3*c - 78*a*b^11*c^2 + 1430*a^2*b^9*c^3 - 8580*a^3*b^7*c^4 + 18018*a^4*b^5*c^5 - 12012*a^5*b^3*c^6 + 1716*a^6*b
*c^7)*x^45 + 1/42*(b^14 - 182*a*b^12*c + 6006*a^2*b^10*c^2 - 60060*a^3*b^8*c^3 + 210210*a^4*b^6*c^4 - 252252*a
^5*b^4*c^5 + 84084*a^6*b^2*c^6 - 3432*a^7*c^7)*x^42 - 1/3*(a*b^13 - 78*a^2*b^11*c + 1430*a^3*b^9*c^2 - 8580*a^
4*b^7*c^3 + 18018*a^5*b^5*c^4 - 12012*a^6*b^3*c^5 + 1716*a^7*b*c^6)*x^39 + 13/6*(a^2*b^12 - 44*a^3*b^10*c + 49
5*a^4*b^8*c^2 - 1848*a^5*b^6*c^3 + 2310*a^6*b^4*c^4 - 792*a^7*b^2*c^5 + 33*a^8*c^6)*x^36 - 13/3*(2*a^3*b^11 -
55*a^4*b^9*c + 396*a^5*b^7*c^2 - 924*a^6*b^5*c^3 + 660*a^7*b^3*c^4 - 99*a^8*b*c^5)*x^33 + 143/6*(a^4*b^10 - 18
*a^5*b^8*c + 84*a^6*b^6*c^2 - 120*a^7*b^4*c^3 + 45*a^8*b^2*c^4 - 2*a^9*c^5)*x^30 - 143/3*(a^5*b^9 - 12*a^6*b^7
*c + 36*a^7*b^5*c^2 - 30*a^8*b^3*c^3 + 5*a^9*b*c^4)*x^27 + 143/6*(3*a^6*b^8 - 24*a^7*b^6*c + 45*a^8*b^4*c^2 -
20*a^9*b^2*c^3 + a^10*c^4)*x^24 - 143/21*(12*a^7*b^7 - 63*a^8*b^5*c + 70*a^9*b^3*c^2 - 14*a^10*b*c^3)*x^21 + 1
3/6*(33*a^8*b^6 - 110*a^9*b^4*c + 66*a^10*b^2*c^2 - 4*a^11*c^3)*x^18 - 1/3*a^13*b*x^3 - 13/3*(11*a^9*b^5 - 22*
a^10*b^3*c + 6*a^11*b*c^2)*x^15 + 13/6*(11*a^10*b^4 - 12*a^11*b^2*c + a^12*c^2)*x^12 - 13/3*(2*a^11*b^3 - a^12
*b*c)*x^9 + 1/6*(13*a^12*b^2 - 2*a^13*c)*x^6

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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 1242 vs. \(2 (18) = 36\).
time = 0.33, size = 1242, normalized size = 62.10 \begin {gather*} \frac {1}{42} \, c^{14} x^{84} + \frac {1}{3} \, b c^{13} x^{81} + \frac {1}{6} \, {\left (13 \, b^{2} c^{12} - 2 \, a c^{13}\right )} x^{78} + \frac {13}{3} \, {\left (2 \, b^{3} c^{11} - a b c^{12}\right )} x^{75} + \frac {13}{6} \, {\left (11 \, b^{4} c^{10} - 12 \, a b^{2} c^{11} + a^{2} c^{12}\right )} x^{72} + \frac {13}{3} \, {\left (11 \, b^{5} c^{9} - 22 \, a b^{3} c^{10} + 6 \, a^{2} b c^{11}\right )} x^{69} + \frac {13}{6} \, {\left (33 \, b^{6} c^{8} - 110 \, a b^{4} c^{9} + 66 \, a^{2} b^{2} c^{10} - 4 \, a^{3} c^{11}\right )} x^{66} + \frac {143}{21} \, {\left (12 \, b^{7} c^{7} - 63 \, a b^{5} c^{8} + 70 \, a^{2} b^{3} c^{9} - 14 \, a^{3} b c^{10}\right )} x^{63} + \frac {143}{6} \, {\left (3 \, b^{8} c^{6} - 24 \, a b^{6} c^{7} + 45 \, a^{2} b^{4} c^{8} - 20 \, a^{3} b^{2} c^{9} + a^{4} c^{10}\right )} x^{60} + \frac {143}{3} \, {\left (b^{9} c^{5} - 12 \, a b^{7} c^{6} + 36 \, a^{2} b^{5} c^{7} - 30 \, a^{3} b^{3} c^{8} + 5 \, a^{4} b c^{9}\right )} x^{57} + \frac {143}{6} \, {\left (b^{10} c^{4} - 18 \, a b^{8} c^{5} + 84 \, a^{2} b^{6} c^{6} - 120 \, a^{3} b^{4} c^{7} + 45 \, a^{4} b^{2} c^{8} - 2 \, a^{5} c^{9}\right )} x^{54} + \frac {13}{3} \, {\left (2 \, b^{11} c^{3} - 55 \, a b^{9} c^{4} + 396 \, a^{2} b^{7} c^{5} - 924 \, a^{3} b^{5} c^{6} + 660 \, a^{4} b^{3} c^{7} - 99 \, a^{5} b c^{8}\right )} x^{51} + \frac {13}{6} \, {\left (b^{12} c^{2} - 44 \, a b^{10} c^{3} + 495 \, a^{2} b^{8} c^{4} - 1848 \, a^{3} b^{6} c^{5} + 2310 \, a^{4} b^{4} c^{6} - 792 \, a^{5} b^{2} c^{7} + 33 \, a^{6} c^{8}\right )} x^{48} + \frac {1}{3} \, {\left (b^{13} c - 78 \, a b^{11} c^{2} + 1430 \, a^{2} b^{9} c^{3} - 8580 \, a^{3} b^{7} c^{4} + 18018 \, a^{4} b^{5} c^{5} - 12012 \, a^{5} b^{3} c^{6} + 1716 \, a^{6} b c^{7}\right )} x^{45} + \frac {1}{42} \, {\left (b^{14} - 182 \, a b^{12} c + 6006 \, a^{2} b^{10} c^{2} - 60060 \, a^{3} b^{8} c^{3} + 210210 \, a^{4} b^{6} c^{4} - 252252 \, a^{5} b^{4} c^{5} + 84084 \, a^{6} b^{2} c^{6} - 3432 \, a^{7} c^{7}\right )} x^{42} - \frac {1}{3} \, {\left (a b^{13} - 78 \, a^{2} b^{11} c + 1430 \, a^{3} b^{9} c^{2} - 8580 \, a^{4} b^{7} c^{3} + 18018 \, a^{5} b^{5} c^{4} - 12012 \, a^{6} b^{3} c^{5} + 1716 \, a^{7} b c^{6}\right )} x^{39} + \frac {13}{6} \, {\left (a^{2} b^{12} - 44 \, a^{3} b^{10} c + 495 \, a^{4} b^{8} c^{2} - 1848 \, a^{5} b^{6} c^{3} + 2310 \, a^{6} b^{4} c^{4} - 792 \, a^{7} b^{2} c^{5} + 33 \, a^{8} c^{6}\right )} x^{36} - \frac {13}{3} \, {\left (2 \, a^{3} b^{11} - 55 \, a^{4} b^{9} c + 396 \, a^{5} b^{7} c^{2} - 924 \, a^{6} b^{5} c^{3} + 660 \, a^{7} b^{3} c^{4} - 99 \, a^{8} b c^{5}\right )} x^{33} + \frac {143}{6} \, {\left (a^{4} b^{10} - 18 \, a^{5} b^{8} c + 84 \, a^{6} b^{6} c^{2} - 120 \, a^{7} b^{4} c^{3} + 45 \, a^{8} b^{2} c^{4} - 2 \, a^{9} c^{5}\right )} x^{30} - \frac {143}{3} \, {\left (a^{5} b^{9} - 12 \, a^{6} b^{7} c + 36 \, a^{7} b^{5} c^{2} - 30 \, a^{8} b^{3} c^{3} + 5 \, a^{9} b c^{4}\right )} x^{27} + \frac {143}{6} \, {\left (3 \, a^{6} b^{8} - 24 \, a^{7} b^{6} c + 45 \, a^{8} b^{4} c^{2} - 20 \, a^{9} b^{2} c^{3} + a^{10} c^{4}\right )} x^{24} - \frac {143}{21} \, {\left (12 \, a^{7} b^{7} - 63 \, a^{8} b^{5} c + 70 \, a^{9} b^{3} c^{2} - 14 \, a^{10} b c^{3}\right )} x^{21} + \frac {13}{6} \, {\left (33 \, a^{8} b^{6} - 110 \, a^{9} b^{4} c + 66 \, a^{10} b^{2} c^{2} - 4 \, a^{11} c^{3}\right )} x^{18} - \frac {1}{3} \, a^{13} b x^{3} - \frac {13}{3} \, {\left (11 \, a^{9} b^{5} - 22 \, a^{10} b^{3} c + 6 \, a^{11} b c^{2}\right )} x^{15} + \frac {13}{6} \, {\left (11 \, a^{10} b^{4} - 12 \, a^{11} b^{2} c + a^{12} c^{2}\right )} x^{12} - \frac {13}{3} \, {\left (2 \, a^{11} b^{3} - a^{12} b c\right )} x^{9} + \frac {1}{6} \, {\left (13 \, a^{12} b^{2} - 2 \, a^{13} c\right )} x^{6} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^2*(2*c*x^3+b)*(c*x^6+b*x^3-a)^13,x, algorithm="fricas")

[Out]

1/42*c^14*x^84 + 1/3*b*c^13*x^81 + 1/6*(13*b^2*c^12 - 2*a*c^13)*x^78 + 13/3*(2*b^3*c^11 - a*b*c^12)*x^75 + 13/
6*(11*b^4*c^10 - 12*a*b^2*c^11 + a^2*c^12)*x^72 + 13/3*(11*b^5*c^9 - 22*a*b^3*c^10 + 6*a^2*b*c^11)*x^69 + 13/6
*(33*b^6*c^8 - 110*a*b^4*c^9 + 66*a^2*b^2*c^10 - 4*a^3*c^11)*x^66 + 143/21*(12*b^7*c^7 - 63*a*b^5*c^8 + 70*a^2
*b^3*c^9 - 14*a^3*b*c^10)*x^63 + 143/6*(3*b^8*c^6 - 24*a*b^6*c^7 + 45*a^2*b^4*c^8 - 20*a^3*b^2*c^9 + a^4*c^10)
*x^60 + 143/3*(b^9*c^5 - 12*a*b^7*c^6 + 36*a^2*b^5*c^7 - 30*a^3*b^3*c^8 + 5*a^4*b*c^9)*x^57 + 143/6*(b^10*c^4
- 18*a*b^8*c^5 + 84*a^2*b^6*c^6 - 120*a^3*b^4*c^7 + 45*a^4*b^2*c^8 - 2*a^5*c^9)*x^54 + 13/3*(2*b^11*c^3 - 55*a
*b^9*c^4 + 396*a^2*b^7*c^5 - 924*a^3*b^5*c^6 + 660*a^4*b^3*c^7 - 99*a^5*b*c^8)*x^51 + 13/6*(b^12*c^2 - 44*a*b^
10*c^3 + 495*a^2*b^8*c^4 - 1848*a^3*b^6*c^5 + 2310*a^4*b^4*c^6 - 792*a^5*b^2*c^7 + 33*a^6*c^8)*x^48 + 1/3*(b^1
3*c - 78*a*b^11*c^2 + 1430*a^2*b^9*c^3 - 8580*a^3*b^7*c^4 + 18018*a^4*b^5*c^5 - 12012*a^5*b^3*c^6 + 1716*a^6*b
*c^7)*x^45 + 1/42*(b^14 - 182*a*b^12*c + 6006*a^2*b^10*c^2 - 60060*a^3*b^8*c^3 + 210210*a^4*b^6*c^4 - 252252*a
^5*b^4*c^5 + 84084*a^6*b^2*c^6 - 3432*a^7*c^7)*x^42 - 1/3*(a*b^13 - 78*a^2*b^11*c + 1430*a^3*b^9*c^2 - 8580*a^
4*b^7*c^3 + 18018*a^5*b^5*c^4 - 12012*a^6*b^3*c^5 + 1716*a^7*b*c^6)*x^39 + 13/6*(a^2*b^12 - 44*a^3*b^10*c + 49
5*a^4*b^8*c^2 - 1848*a^5*b^6*c^3 + 2310*a^6*b^4*c^4 - 792*a^7*b^2*c^5 + 33*a^8*c^6)*x^36 - 13/3*(2*a^3*b^11 -
55*a^4*b^9*c + 396*a^5*b^7*c^2 - 924*a^6*b^5*c^3 + 660*a^7*b^3*c^4 - 99*a^8*b*c^5)*x^33 + 143/6*(a^4*b^10 - 18
*a^5*b^8*c + 84*a^6*b^6*c^2 - 120*a^7*b^4*c^3 + 45*a^8*b^2*c^4 - 2*a^9*c^5)*x^30 - 143/3*(a^5*b^9 - 12*a^6*b^7
*c + 36*a^7*b^5*c^2 - 30*a^8*b^3*c^3 + 5*a^9*b*c^4)*x^27 + 143/6*(3*a^6*b^8 - 24*a^7*b^6*c + 45*a^8*b^4*c^2 -
20*a^9*b^2*c^3 + a^10*c^4)*x^24 - 143/21*(12*a^7*b^7 - 63*a^8*b^5*c + 70*a^9*b^3*c^2 - 14*a^10*b*c^3)*x^21 + 1
3/6*(33*a^8*b^6 - 110*a^9*b^4*c + 66*a^10*b^2*c^2 - 4*a^11*c^3)*x^18 - 1/3*a^13*b*x^3 - 13/3*(11*a^9*b^5 - 22*
a^10*b^3*c + 6*a^11*b*c^2)*x^15 + 13/6*(11*a^10*b^4 - 12*a^11*b^2*c + a^12*c^2)*x^12 - 13/3*(2*a^11*b^3 - a^12
*b*c)*x^9 + 1/6*(13*a^12*b^2 - 2*a^13*c)*x^6

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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 1394 vs. \(2 (14) = 28\).
time = 0.15, size = 1394, normalized size = 69.70 \begin {gather*} - \frac {a^{13} b x^{3}}{3} + \frac {b c^{13} x^{81}}{3} + \frac {c^{14} x^{84}}{42} + x^{78} \left (- \frac {a c^{13}}{3} + \frac {13 b^{2} c^{12}}{6}\right ) + x^{75} \left (- \frac {13 a b c^{12}}{3} + \frac {26 b^{3} c^{11}}{3}\right ) + x^{72} \cdot \left (\frac {13 a^{2} c^{12}}{6} - 26 a b^{2} c^{11} + \frac {143 b^{4} c^{10}}{6}\right ) + x^{69} \cdot \left (26 a^{2} b c^{11} - \frac {286 a b^{3} c^{10}}{3} + \frac {143 b^{5} c^{9}}{3}\right ) + x^{66} \left (- \frac {26 a^{3} c^{11}}{3} + 143 a^{2} b^{2} c^{10} - \frac {715 a b^{4} c^{9}}{3} + \frac {143 b^{6} c^{8}}{2}\right ) + x^{63} \left (- \frac {286 a^{3} b c^{10}}{3} + \frac {1430 a^{2} b^{3} c^{9}}{3} - 429 a b^{5} c^{8} + \frac {572 b^{7} c^{7}}{7}\right ) + x^{60} \cdot \left (\frac {143 a^{4} c^{10}}{6} - \frac {1430 a^{3} b^{2} c^{9}}{3} + \frac {2145 a^{2} b^{4} c^{8}}{2} - 572 a b^{6} c^{7} + \frac {143 b^{8} c^{6}}{2}\right ) + x^{57} \cdot \left (\frac {715 a^{4} b c^{9}}{3} - 1430 a^{3} b^{3} c^{8} + 1716 a^{2} b^{5} c^{7} - 572 a b^{7} c^{6} + \frac {143 b^{9} c^{5}}{3}\right ) + x^{54} \left (- \frac {143 a^{5} c^{9}}{3} + \frac {2145 a^{4} b^{2} c^{8}}{2} - 2860 a^{3} b^{4} c^{7} + 2002 a^{2} b^{6} c^{6} - 429 a b^{8} c^{5} + \frac {143 b^{10} c^{4}}{6}\right ) + x^{51} \left (- 429 a^{5} b c^{8} + 2860 a^{4} b^{3} c^{7} - 4004 a^{3} b^{5} c^{6} + 1716 a^{2} b^{7} c^{5} - \frac {715 a b^{9} c^{4}}{3} + \frac {26 b^{11} c^{3}}{3}\right ) + x^{48} \cdot \left (\frac {143 a^{6} c^{8}}{2} - 1716 a^{5} b^{2} c^{7} + 5005 a^{4} b^{4} c^{6} - 4004 a^{3} b^{6} c^{5} + \frac {2145 a^{2} b^{8} c^{4}}{2} - \frac {286 a b^{10} c^{3}}{3} + \frac {13 b^{12} c^{2}}{6}\right ) + x^{45} \cdot \left (572 a^{6} b c^{7} - 4004 a^{5} b^{3} c^{6} + 6006 a^{4} b^{5} c^{5} - 2860 a^{3} b^{7} c^{4} + \frac {1430 a^{2} b^{9} c^{3}}{3} - 26 a b^{11} c^{2} + \frac {b^{13} c}{3}\right ) + x^{42} \left (- \frac {572 a^{7} c^{7}}{7} + 2002 a^{6} b^{2} c^{6} - 6006 a^{5} b^{4} c^{5} + 5005 a^{4} b^{6} c^{4} - 1430 a^{3} b^{8} c^{3} + 143 a^{2} b^{10} c^{2} - \frac {13 a b^{12} c}{3} + \frac {b^{14}}{42}\right ) + x^{39} \left (- 572 a^{7} b c^{6} + 4004 a^{6} b^{3} c^{5} - 6006 a^{5} b^{5} c^{4} + 2860 a^{4} b^{7} c^{3} - \frac {1430 a^{3} b^{9} c^{2}}{3} + 26 a^{2} b^{11} c - \frac {a b^{13}}{3}\right ) + x^{36} \cdot \left (\frac {143 a^{8} c^{6}}{2} - 1716 a^{7} b^{2} c^{5} + 5005 a^{6} b^{4} c^{4} - 4004 a^{5} b^{6} c^{3} + \frac {2145 a^{4} b^{8} c^{2}}{2} - \frac {286 a^{3} b^{10} c}{3} + \frac {13 a^{2} b^{12}}{6}\right ) + x^{33} \cdot \left (429 a^{8} b c^{5} - 2860 a^{7} b^{3} c^{4} + 4004 a^{6} b^{5} c^{3} - 1716 a^{5} b^{7} c^{2} + \frac {715 a^{4} b^{9} c}{3} - \frac {26 a^{3} b^{11}}{3}\right ) + x^{30} \left (- \frac {143 a^{9} c^{5}}{3} + \frac {2145 a^{8} b^{2} c^{4}}{2} - 2860 a^{7} b^{4} c^{3} + 2002 a^{6} b^{6} c^{2} - 429 a^{5} b^{8} c + \frac {143 a^{4} b^{10}}{6}\right ) + x^{27} \left (- \frac {715 a^{9} b c^{4}}{3} + 1430 a^{8} b^{3} c^{3} - 1716 a^{7} b^{5} c^{2} + 572 a^{6} b^{7} c - \frac {143 a^{5} b^{9}}{3}\right ) + x^{24} \cdot \left (\frac {143 a^{10} c^{4}}{6} - \frac {1430 a^{9} b^{2} c^{3}}{3} + \frac {2145 a^{8} b^{4} c^{2}}{2} - 572 a^{7} b^{6} c + \frac {143 a^{6} b^{8}}{2}\right ) + x^{21} \cdot \left (\frac {286 a^{10} b c^{3}}{3} - \frac {1430 a^{9} b^{3} c^{2}}{3} + 429 a^{8} b^{5} c - \frac {572 a^{7} b^{7}}{7}\right ) + x^{18} \left (- \frac {26 a^{11} c^{3}}{3} + 143 a^{10} b^{2} c^{2} - \frac {715 a^{9} b^{4} c}{3} + \frac {143 a^{8} b^{6}}{2}\right ) + x^{15} \left (- 26 a^{11} b c^{2} + \frac {286 a^{10} b^{3} c}{3} - \frac {143 a^{9} b^{5}}{3}\right ) + x^{12} \cdot \left (\frac {13 a^{12} c^{2}}{6} - 26 a^{11} b^{2} c + \frac {143 a^{10} b^{4}}{6}\right ) + x^{9} \cdot \left (\frac {13 a^{12} b c}{3} - \frac {26 a^{11} b^{3}}{3}\right ) + x^{6} \left (- \frac {a^{13} c}{3} + \frac {13 a^{12} b^{2}}{6}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**2*(2*c*x**3+b)*(c*x**6+b*x**3-a)**13,x)

[Out]

-a**13*b*x**3/3 + b*c**13*x**81/3 + c**14*x**84/42 + x**78*(-a*c**13/3 + 13*b**2*c**12/6) + x**75*(-13*a*b*c**
12/3 + 26*b**3*c**11/3) + x**72*(13*a**2*c**12/6 - 26*a*b**2*c**11 + 143*b**4*c**10/6) + x**69*(26*a**2*b*c**1
1 - 286*a*b**3*c**10/3 + 143*b**5*c**9/3) + x**66*(-26*a**3*c**11/3 + 143*a**2*b**2*c**10 - 715*a*b**4*c**9/3
+ 143*b**6*c**8/2) + x**63*(-286*a**3*b*c**10/3 + 1430*a**2*b**3*c**9/3 - 429*a*b**5*c**8 + 572*b**7*c**7/7) +
x**60*(143*a**4*c**10/6 - 1430*a**3*b**2*c**9/3 + 2145*a**2*b**4*c**8/2 - 572*a*b**6*c**7 + 143*b**8*c**6/2)
+ x**57*(715*a**4*b*c**9/3 - 1430*a**3*b**3*c**8 + 1716*a**2*b**5*c**7 - 572*a*b**7*c**6 + 143*b**9*c**5/3) +
x**54*(-143*a**5*c**9/3 + 2145*a**4*b**2*c**8/2 - 2860*a**3*b**4*c**7 + 2002*a**2*b**6*c**6 - 429*a*b**8*c**5
+ 143*b**10*c**4/6) + x**51*(-429*a**5*b*c**8 + 2860*a**4*b**3*c**7 - 4004*a**3*b**5*c**6 + 1716*a**2*b**7*c**
5 - 715*a*b**9*c**4/3 + 26*b**11*c**3/3) + x**48*(143*a**6*c**8/2 - 1716*a**5*b**2*c**7 + 5005*a**4*b**4*c**6
- 4004*a**3*b**6*c**5 + 2145*a**2*b**8*c**4/2 - 286*a*b**10*c**3/3 + 13*b**12*c**2/6) + x**45*(572*a**6*b*c**7
- 4004*a**5*b**3*c**6 + 6006*a**4*b**5*c**5 - 2860*a**3*b**7*c**4 + 1430*a**2*b**9*c**3/3 - 26*a*b**11*c**2 +
b**13*c/3) + x**42*(-572*a**7*c**7/7 + 2002*a**6*b**2*c**6 - 6006*a**5*b**4*c**5 + 5005*a**4*b**6*c**4 - 1430
*a**3*b**8*c**3 + 143*a**2*b**10*c**2 - 13*a*b**12*c/3 + b**14/42) + x**39*(-572*a**7*b*c**6 + 4004*a**6*b**3*
c**5 - 6006*a**5*b**5*c**4 + 2860*a**4*b**7*c**3 - 1430*a**3*b**9*c**2/3 + 26*a**2*b**11*c - a*b**13/3) + x**3
6*(143*a**8*c**6/2 - 1716*a**7*b**2*c**5 + 5005*a**6*b**4*c**4 - 4004*a**5*b**6*c**3 + 2145*a**4*b**8*c**2/2 -
286*a**3*b**10*c/3 + 13*a**2*b**12/6) + x**33*(429*a**8*b*c**5 - 2860*a**7*b**3*c**4 + 4004*a**6*b**5*c**3 -
1716*a**5*b**7*c**2 + 715*a**4*b**9*c/3 - 26*a**3*b**11/3) + x**30*(-143*a**9*c**5/3 + 2145*a**8*b**2*c**4/2 -
2860*a**7*b**4*c**3 + 2002*a**6*b**6*c**2 - 429*a**5*b**8*c + 143*a**4*b**10/6) + x**27*(-715*a**9*b*c**4/3 +
1430*a**8*b**3*c**3 - 1716*a**7*b**5*c**2 + 572*a**6*b**7*c - 143*a**5*b**9/3) + x**24*(143*a**10*c**4/6 - 14
30*a**9*b**2*c**3/3 + 2145*a**8*b**4*c**2/2 - 572*a**7*b**6*c + 143*a**6*b**8/2) + x**21*(286*a**10*b*c**3/3 -
1430*a**9*b**3*c**2/3 + 429*a**8*b**5*c - 572*a**7*b**7/7) + x**18*(-26*a**11*c**3/3 + 143*a**10*b**2*c**2 -
715*a**9*b**4*c/3 + 143*a**8*b**6/2) + x**15*(-26*a**11*b*c**2 + 286*a**10*b**3*c/3 - 143*a**9*b**5/3) + x**12
*(13*a**12*c**2/6 - 26*a**11*b**2*c + 143*a**10*b**4/6) + x**9*(13*a**12*b*c/3 - 26*a**11*b**3/3) + x**6*(-a**
13*c/3 + 13*a**12*b**2/6)

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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 246 vs. \(2 (18) = 36\).
time = 5.50, size = 246, normalized size = 12.30 \begin {gather*} \frac {1}{42} \, {\left (c x^{6} + b x^{3}\right )}^{14} - \frac {1}{3} \, {\left (c x^{6} + b x^{3}\right )}^{13} a + \frac {13}{6} \, {\left (c x^{6} + b x^{3}\right )}^{12} a^{2} - \frac {26}{3} \, {\left (c x^{6} + b x^{3}\right )}^{11} a^{3} + \frac {143}{6} \, {\left (c x^{6} + b x^{3}\right )}^{10} a^{4} - \frac {143}{3} \, {\left (c x^{6} + b x^{3}\right )}^{9} a^{5} + \frac {143}{2} \, {\left (c x^{6} + b x^{3}\right )}^{8} a^{6} - \frac {572}{7} \, {\left (c x^{6} + b x^{3}\right )}^{7} a^{7} + \frac {143}{2} \, {\left (c x^{6} + b x^{3}\right )}^{6} a^{8} - \frac {143}{3} \, {\left (c x^{6} + b x^{3}\right )}^{5} a^{9} + \frac {143}{6} \, {\left (c x^{6} + b x^{3}\right )}^{4} a^{10} - \frac {26}{3} \, {\left (c x^{6} + b x^{3}\right )}^{3} a^{11} + \frac {13}{6} \, {\left (c x^{6} + b x^{3}\right )}^{2} a^{12} - \frac {1}{3} \, {\left (c x^{6} + b x^{3}\right )} a^{13} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^2*(2*c*x^3+b)*(c*x^6+b*x^3-a)^13,x, algorithm="giac")

[Out]

1/42*(c*x^6 + b*x^3)^14 - 1/3*(c*x^6 + b*x^3)^13*a + 13/6*(c*x^6 + b*x^3)^12*a^2 - 26/3*(c*x^6 + b*x^3)^11*a^3
+ 143/6*(c*x^6 + b*x^3)^10*a^4 - 143/3*(c*x^6 + b*x^3)^9*a^5 + 143/2*(c*x^6 + b*x^3)^8*a^6 - 572/7*(c*x^6 + b
*x^3)^7*a^7 + 143/2*(c*x^6 + b*x^3)^6*a^8 - 143/3*(c*x^6 + b*x^3)^5*a^9 + 143/6*(c*x^6 + b*x^3)^4*a^10 - 26/3*
(c*x^6 + b*x^3)^3*a^11 + 13/6*(c*x^6 + b*x^3)^2*a^12 - 1/3*(c*x^6 + b*x^3)*a^13

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Mupad [B]
time = 1.28, size = 1214, normalized size = 60.70 \begin {gather*} x^{36}\,\left (\frac {143\,a^8\,c^6}{2}-1716\,a^7\,b^2\,c^5+5005\,a^6\,b^4\,c^4-4004\,a^5\,b^6\,c^3+\frac {2145\,a^4\,b^8\,c^2}{2}-\frac {286\,a^3\,b^{10}\,c}{3}+\frac {13\,a^2\,b^{12}}{6}\right )+x^{48}\,\left (\frac {143\,a^6\,c^8}{2}-1716\,a^5\,b^2\,c^7+5005\,a^4\,b^4\,c^6-4004\,a^3\,b^6\,c^5+\frac {2145\,a^2\,b^8\,c^4}{2}-\frac {286\,a\,b^{10}\,c^3}{3}+\frac {13\,b^{12}\,c^2}{6}\right )-x^{39}\,\left (572\,a^7\,b\,c^6-4004\,a^6\,b^3\,c^5+6006\,a^5\,b^5\,c^4-2860\,a^4\,b^7\,c^3+\frac {1430\,a^3\,b^9\,c^2}{3}-26\,a^2\,b^{11}\,c+\frac {a\,b^{13}}{3}\right )+x^{45}\,\left (572\,a^6\,b\,c^7-4004\,a^5\,b^3\,c^6+6006\,a^4\,b^5\,c^5-2860\,a^3\,b^7\,c^4+\frac {1430\,a^2\,b^9\,c^3}{3}-26\,a\,b^{11}\,c^2+\frac {b^{13}\,c}{3}\right )+x^{18}\,\left (-\frac {26\,a^{11}\,c^3}{3}+143\,a^{10}\,b^2\,c^2-\frac {715\,a^9\,b^4\,c}{3}+\frac {143\,a^8\,b^6}{2}\right )-x^{66}\,\left (\frac {26\,a^3\,c^{11}}{3}-143\,a^2\,b^2\,c^{10}+\frac {715\,a\,b^4\,c^9}{3}-\frac {143\,b^6\,c^8}{2}\right )+x^{30}\,\left (-\frac {143\,a^9\,c^5}{3}+\frac {2145\,a^8\,b^2\,c^4}{2}-2860\,a^7\,b^4\,c^3+2002\,a^6\,b^6\,c^2-429\,a^5\,b^8\,c+\frac {143\,a^4\,b^{10}}{6}\right )-x^{54}\,\left (\frac {143\,a^5\,c^9}{3}-\frac {2145\,a^4\,b^2\,c^8}{2}+2860\,a^3\,b^4\,c^7-2002\,a^2\,b^6\,c^6+429\,a\,b^8\,c^5-\frac {143\,b^{10}\,c^4}{6}\right )+x^{42}\,\left (-\frac {572\,a^7\,c^7}{7}+2002\,a^6\,b^2\,c^6-6006\,a^5\,b^4\,c^5+5005\,a^4\,b^6\,c^4-1430\,a^3\,b^8\,c^3+143\,a^2\,b^{10}\,c^2-\frac {13\,a\,b^{12}\,c}{3}+\frac {b^{14}}{42}\right )+x^{24}\,\left (\frac {143\,a^{10}\,c^4}{6}-\frac {1430\,a^9\,b^2\,c^3}{3}+\frac {2145\,a^8\,b^4\,c^2}{2}-572\,a^7\,b^6\,c+\frac {143\,a^6\,b^8}{2}\right )+x^{60}\,\left (\frac {143\,a^4\,c^{10}}{6}-\frac {1430\,a^3\,b^2\,c^9}{3}+\frac {2145\,a^2\,b^4\,c^8}{2}-572\,a\,b^6\,c^7+\frac {143\,b^8\,c^6}{2}\right )+\frac {c^{14}\,x^{84}}{42}-x^6\,\left (\frac {a^{13}\,c}{3}-\frac {13\,a^{12}\,b^2}{6}\right )+\frac {13\,a^{10}\,x^{12}\,\left (a^2\,c^2-12\,a\,b^2\,c+11\,b^4\right )}{6}+\frac {13\,c^{10}\,x^{72}\,\left (a^2\,c^2-12\,a\,b^2\,c+11\,b^4\right )}{6}-\frac {a^{13}\,b\,x^3}{3}+\frac {b\,c^{13}\,x^{81}}{3}-\frac {c^{12}\,x^{78}\,\left (2\,a\,c-13\,b^2\right )}{6}-\frac {143\,a^7\,b\,x^{21}\,\left (-14\,a^3\,c^3+70\,a^2\,b^2\,c^2-63\,a\,b^4\,c+12\,b^6\right )}{21}+\frac {143\,b\,c^7\,x^{63}\,\left (-14\,a^3\,c^3+70\,a^2\,b^2\,c^2-63\,a\,b^4\,c+12\,b^6\right )}{21}-\frac {143\,a^5\,b\,x^{27}\,\left (5\,a^4\,c^4-30\,a^3\,b^2\,c^3+36\,a^2\,b^4\,c^2-12\,a\,b^6\,c+b^8\right )}{3}+\frac {143\,b\,c^5\,x^{57}\,\left (5\,a^4\,c^4-30\,a^3\,b^2\,c^3+36\,a^2\,b^4\,c^2-12\,a\,b^6\,c+b^8\right )}{3}-\frac {13\,a^3\,b\,x^{33}\,\left (-99\,a^5\,c^5+660\,a^4\,b^2\,c^4-924\,a^3\,b^4\,c^3+396\,a^2\,b^6\,c^2-55\,a\,b^8\,c+2\,b^{10}\right )}{3}+\frac {13\,b\,c^3\,x^{51}\,\left (-99\,a^5\,c^5+660\,a^4\,b^2\,c^4-924\,a^3\,b^4\,c^3+396\,a^2\,b^6\,c^2-55\,a\,b^8\,c+2\,b^{10}\right )}{3}-\frac {13\,a^9\,b\,x^{15}\,\left (6\,a^2\,c^2-22\,a\,b^2\,c+11\,b^4\right )}{3}+\frac {13\,b\,c^9\,x^{69}\,\left (6\,a^2\,c^2-22\,a\,b^2\,c+11\,b^4\right )}{3}+\frac {13\,a^{11}\,b\,x^9\,\left (a\,c-2\,b^2\right )}{3}-\frac {13\,b\,c^{11}\,x^{75}\,\left (a\,c-2\,b^2\right )}{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^2*(b + 2*c*x^3)*(b*x^3 - a + c*x^6)^13,x)

[Out]

x^36*((13*a^2*b^12)/6 + (143*a^8*c^6)/2 - (286*a^3*b^10*c)/3 + (2145*a^4*b^8*c^2)/2 - 4004*a^5*b^6*c^3 + 5005*
a^6*b^4*c^4 - 1716*a^7*b^2*c^5) + x^48*((143*a^6*c^8)/2 + (13*b^12*c^2)/6 - (286*a*b^10*c^3)/3 + (2145*a^2*b^8
*c^4)/2 - 4004*a^3*b^6*c^5 + 5005*a^4*b^4*c^6 - 1716*a^5*b^2*c^7) - x^39*((a*b^13)/3 - 26*a^2*b^11*c + 572*a^7
*b*c^6 + (1430*a^3*b^9*c^2)/3 - 2860*a^4*b^7*c^3 + 6006*a^5*b^5*c^4 - 4004*a^6*b^3*c^5) + x^45*((b^13*c)/3 - 2
6*a*b^11*c^2 + 572*a^6*b*c^7 + (1430*a^2*b^9*c^3)/3 - 2860*a^3*b^7*c^4 + 6006*a^4*b^5*c^5 - 4004*a^5*b^3*c^6)
+ x^18*((143*a^8*b^6)/2 - (26*a^11*c^3)/3 - (715*a^9*b^4*c)/3 + 143*a^10*b^2*c^2) - x^66*((26*a^3*c^11)/3 - (1
43*b^6*c^8)/2 + (715*a*b^4*c^9)/3 - 143*a^2*b^2*c^10) + x^30*((143*a^4*b^10)/6 - (143*a^9*c^5)/3 - 429*a^5*b^8
*c + 2002*a^6*b^6*c^2 - 2860*a^7*b^4*c^3 + (2145*a^8*b^2*c^4)/2) - x^54*((143*a^5*c^9)/3 - (143*b^10*c^4)/6 +
429*a*b^8*c^5 - 2002*a^2*b^6*c^6 + 2860*a^3*b^4*c^7 - (2145*a^4*b^2*c^8)/2) + x^42*(b^14/42 - (572*a^7*c^7)/7
+ 143*a^2*b^10*c^2 - 1430*a^3*b^8*c^3 + 5005*a^4*b^6*c^4 - 6006*a^5*b^4*c^5 + 2002*a^6*b^2*c^6 - (13*a*b^12*c)
/3) + x^24*((143*a^6*b^8)/2 + (143*a^10*c^4)/6 - 572*a^7*b^6*c + (2145*a^8*b^4*c^2)/2 - (1430*a^9*b^2*c^3)/3)
+ x^60*((143*a^4*c^10)/6 + (143*b^8*c^6)/2 - 572*a*b^6*c^7 + (2145*a^2*b^4*c^8)/2 - (1430*a^3*b^2*c^9)/3) + (c
^14*x^84)/42 - x^6*((a^13*c)/3 - (13*a^12*b^2)/6) + (13*a^10*x^12*(11*b^4 + a^2*c^2 - 12*a*b^2*c))/6 + (13*c^1
0*x^72*(11*b^4 + a^2*c^2 - 12*a*b^2*c))/6 - (a^13*b*x^3)/3 + (b*c^13*x^81)/3 - (c^12*x^78*(2*a*c - 13*b^2))/6
- (143*a^7*b*x^21*(12*b^6 - 14*a^3*c^3 + 70*a^2*b^2*c^2 - 63*a*b^4*c))/21 + (143*b*c^7*x^63*(12*b^6 - 14*a^3*c
^3 + 70*a^2*b^2*c^2 - 63*a*b^4*c))/21 - (143*a^5*b*x^27*(b^8 + 5*a^4*c^4 + 36*a^2*b^4*c^2 - 30*a^3*b^2*c^3 - 1
2*a*b^6*c))/3 + (143*b*c^5*x^57*(b^8 + 5*a^4*c^4 + 36*a^2*b^4*c^2 - 30*a^3*b^2*c^3 - 12*a*b^6*c))/3 - (13*a^3*
b*x^33*(2*b^10 - 99*a^5*c^5 + 396*a^2*b^6*c^2 - 924*a^3*b^4*c^3 + 660*a^4*b^2*c^4 - 55*a*b^8*c))/3 + (13*b*c^3
*x^51*(2*b^10 - 99*a^5*c^5 + 396*a^2*b^6*c^2 - 924*a^3*b^4*c^3 + 660*a^4*b^2*c^4 - 55*a*b^8*c))/3 - (13*a^9*b*
x^15*(11*b^4 + 6*a^2*c^2 - 22*a*b^2*c))/3 + (13*b*c^9*x^69*(11*b^4 + 6*a^2*c^2 - 22*a*b^2*c))/3 + (13*a^11*b*x
^9*(a*c - 2*b^2))/3 - (13*b*c^11*x^75*(a*c - 2*b^2))/3

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