Optimal. Leaf size=16 \[ \frac {1}{42} x^{42} \left (b+c x^3\right )^{14} \]
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Rubi [A]
time = 0.03, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 3, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.120, Rules used = {1598, 457, 75}
\begin {gather*} \frac {1}{42} x^{42} \left (b+c x^3\right )^{14} \end {gather*}
Antiderivative was successfully verified.
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Rule 75
Rule 457
Rule 1598
Rubi steps
\begin {align*} \int x^2 \left (b+2 c x^3\right ) \left (b x^3+c x^6\right )^{13} \, dx &=\int x^{41} \left (b+c x^3\right )^{13} \left (b+2 c x^3\right ) \, dx\\ &=\frac {1}{3} \text {Subst}\left (\int x^{13} (b+c x)^{13} (b+2 c x) \, dx,x,x^3\right )\\ &=\frac {1}{42} x^{42} \left (b+c x^3\right )^{14}\\ \end {align*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(186\) vs. \(2(16)=32\).
time = 0.00, size = 186, normalized size = 11.62 \begin {gather*} \frac {b^{14} x^{42}}{42}+\frac {1}{3} b^{13} c x^{45}+\frac {13}{6} b^{12} c^2 x^{48}+\frac {26}{3} b^{11} c^3 x^{51}+\frac {143}{6} b^{10} c^4 x^{54}+\frac {143}{3} b^9 c^5 x^{57}+\frac {143}{2} b^8 c^6 x^{60}+\frac {572}{7} b^7 c^7 x^{63}+\frac {143}{2} b^6 c^8 x^{66}+\frac {143}{3} b^5 c^9 x^{69}+\frac {143}{6} b^4 c^{10} x^{72}+\frac {26}{3} b^3 c^{11} x^{75}+\frac {13}{6} b^2 c^{12} x^{78}+\frac {1}{3} b c^{13} x^{81}+\frac {c^{14} x^{84}}{42} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.26, size = 24, normalized size = 1.50
method | result | size |
gosper | \(\frac {x^{42} \left (c \,x^{3}+b \right )^{14}}{42}\) | \(15\) |
default | \(\frac {\left (b^{2}-\left (2 c \,x^{3}+b \right )^{2}\right )^{14}}{11274289152 c^{14}}\) | \(24\) |
risch | \(\frac {26}{3} x^{75} b^{3} c^{11}+\frac {13}{6} x^{78} b^{2} c^{12}+\frac {1}{3} b \,c^{13} x^{81}+\frac {1}{42} c^{14} x^{84}+\frac {143}{2} x^{66} b^{6} c^{8}+\frac {143}{3} x^{69} b^{5} c^{9}+\frac {143}{6} x^{72} b^{4} c^{10}+\frac {143}{2} x^{60} b^{8} c^{6}+\frac {572}{7} x^{63} b^{7} c^{7}+\frac {143}{3} x^{57} b^{9} c^{5}+\frac {26}{3} x^{51} b^{11} c^{3}+\frac {143}{6} x^{54} b^{10} c^{4}+\frac {13}{6} x^{48} b^{12} c^{2}+\frac {1}{42} x^{42} b^{14}+\frac {1}{3} x^{45} b^{13} c\) | \(157\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 156 vs.
\(2 (14) = 28\).
time = 0.28, size = 156, normalized size = 9.75 \begin {gather*} \frac {1}{42} \, c^{14} x^{84} + \frac {1}{3} \, b c^{13} x^{81} + \frac {13}{6} \, b^{2} c^{12} x^{78} + \frac {26}{3} \, b^{3} c^{11} x^{75} + \frac {143}{6} \, b^{4} c^{10} x^{72} + \frac {143}{3} \, b^{5} c^{9} x^{69} + \frac {143}{2} \, b^{6} c^{8} x^{66} + \frac {572}{7} \, b^{7} c^{7} x^{63} + \frac {143}{2} \, b^{8} c^{6} x^{60} + \frac {143}{3} \, b^{9} c^{5} x^{57} + \frac {143}{6} \, b^{10} c^{4} x^{54} + \frac {26}{3} \, b^{11} c^{3} x^{51} + \frac {13}{6} \, b^{12} c^{2} x^{48} + \frac {1}{3} \, b^{13} c x^{45} + \frac {1}{42} \, b^{14} x^{42} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 156 vs.
\(2 (14) = 28\).
time = 0.33, size = 156, normalized size = 9.75 \begin {gather*} \frac {1}{42} \, c^{14} x^{84} + \frac {1}{3} \, b c^{13} x^{81} + \frac {13}{6} \, b^{2} c^{12} x^{78} + \frac {26}{3} \, b^{3} c^{11} x^{75} + \frac {143}{6} \, b^{4} c^{10} x^{72} + \frac {143}{3} \, b^{5} c^{9} x^{69} + \frac {143}{2} \, b^{6} c^{8} x^{66} + \frac {572}{7} \, b^{7} c^{7} x^{63} + \frac {143}{2} \, b^{8} c^{6} x^{60} + \frac {143}{3} \, b^{9} c^{5} x^{57} + \frac {143}{6} \, b^{10} c^{4} x^{54} + \frac {26}{3} \, b^{11} c^{3} x^{51} + \frac {13}{6} \, b^{12} c^{2} x^{48} + \frac {1}{3} \, b^{13} c x^{45} + \frac {1}{42} \, b^{14} x^{42} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 185 vs.
\(2 (12) = 24\).
time = 0.04, size = 185, normalized size = 11.56 \begin {gather*} \frac {b^{14} x^{42}}{42} + \frac {b^{13} c x^{45}}{3} + \frac {13 b^{12} c^{2} x^{48}}{6} + \frac {26 b^{11} c^{3} x^{51}}{3} + \frac {143 b^{10} c^{4} x^{54}}{6} + \frac {143 b^{9} c^{5} x^{57}}{3} + \frac {143 b^{8} c^{6} x^{60}}{2} + \frac {572 b^{7} c^{7} x^{63}}{7} + \frac {143 b^{6} c^{8} x^{66}}{2} + \frac {143 b^{5} c^{9} x^{69}}{3} + \frac {143 b^{4} c^{10} x^{72}}{6} + \frac {26 b^{3} c^{11} x^{75}}{3} + \frac {13 b^{2} c^{12} x^{78}}{6} + \frac {b c^{13} x^{81}}{3} + \frac {c^{14} x^{84}}{42} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 3.50, size = 15, normalized size = 0.94 \begin {gather*} \frac {1}{42} \, {\left (c x^{6} + b x^{3}\right )}^{14} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 2.08, size = 156, normalized size = 9.75 \begin {gather*} \frac {b^{14}\,x^{42}}{42}+\frac {b^{13}\,c\,x^{45}}{3}+\frac {13\,b^{12}\,c^2\,x^{48}}{6}+\frac {26\,b^{11}\,c^3\,x^{51}}{3}+\frac {143\,b^{10}\,c^4\,x^{54}}{6}+\frac {143\,b^9\,c^5\,x^{57}}{3}+\frac {143\,b^8\,c^6\,x^{60}}{2}+\frac {572\,b^7\,c^7\,x^{63}}{7}+\frac {143\,b^6\,c^8\,x^{66}}{2}+\frac {143\,b^5\,c^9\,x^{69}}{3}+\frac {143\,b^4\,c^{10}\,x^{72}}{6}+\frac {26\,b^3\,c^{11}\,x^{75}}{3}+\frac {13\,b^2\,c^{12}\,x^{78}}{6}+\frac {b\,c^{13}\,x^{81}}{3}+\frac {c^{14}\,x^{84}}{42} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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