Optimal. Leaf size=69 \[ \frac {a^5 x^{15}}{15}+\frac {5}{18} a^4 b x^{18}+\frac {10}{21} a^3 b^2 x^{21}+\frac {5}{12} a^2 b^3 x^{24}+\frac {5}{27} a b^4 x^{27}+\frac {b^5 x^{30}}{30} \]
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Rubi [A]
time = 0.03, antiderivative size = 69, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {272, 45}
\begin {gather*} \frac {a^5 x^{15}}{15}+\frac {5}{18} a^4 b x^{18}+\frac {10}{21} a^3 b^2 x^{21}+\frac {5}{12} a^2 b^3 x^{24}+\frac {5}{27} a b^4 x^{27}+\frac {b^5 x^{30}}{30} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rule 272
Rubi steps
\begin {align*} \int x^{14} \left (a+b x^3\right )^5 \, dx &=\frac {1}{3} \text {Subst}\left (\int x^4 (a+b x)^5 \, dx,x,x^3\right )\\ &=\frac {1}{3} \text {Subst}\left (\int \left (a^5 x^4+5 a^4 b x^5+10 a^3 b^2 x^6+10 a^2 b^3 x^7+5 a b^4 x^8+b^5 x^9\right ) \, dx,x,x^3\right )\\ &=\frac {a^5 x^{15}}{15}+\frac {5}{18} a^4 b x^{18}+\frac {10}{21} a^3 b^2 x^{21}+\frac {5}{12} a^2 b^3 x^{24}+\frac {5}{27} a b^4 x^{27}+\frac {b^5 x^{30}}{30}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 69, normalized size = 1.00 \begin {gather*} \frac {a^5 x^{15}}{15}+\frac {5}{18} a^4 b x^{18}+\frac {10}{21} a^3 b^2 x^{21}+\frac {5}{12} a^2 b^3 x^{24}+\frac {5}{27} a b^4 x^{27}+\frac {b^5 x^{30}}{30} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.13, size = 58, normalized size = 0.84
method | result | size |
gosper | \(\frac {1}{15} a^{5} x^{15}+\frac {5}{18} a^{4} b \,x^{18}+\frac {10}{21} a^{3} b^{2} x^{21}+\frac {5}{12} a^{2} b^{3} x^{24}+\frac {5}{27} a \,b^{4} x^{27}+\frac {1}{30} b^{5} x^{30}\) | \(58\) |
default | \(\frac {1}{15} a^{5} x^{15}+\frac {5}{18} a^{4} b \,x^{18}+\frac {10}{21} a^{3} b^{2} x^{21}+\frac {5}{12} a^{2} b^{3} x^{24}+\frac {5}{27} a \,b^{4} x^{27}+\frac {1}{30} b^{5} x^{30}\) | \(58\) |
norman | \(\frac {1}{15} a^{5} x^{15}+\frac {5}{18} a^{4} b \,x^{18}+\frac {10}{21} a^{3} b^{2} x^{21}+\frac {5}{12} a^{2} b^{3} x^{24}+\frac {5}{27} a \,b^{4} x^{27}+\frac {1}{30} b^{5} x^{30}\) | \(58\) |
risch | \(\frac {1}{15} a^{5} x^{15}+\frac {5}{18} a^{4} b \,x^{18}+\frac {10}{21} a^{3} b^{2} x^{21}+\frac {5}{12} a^{2} b^{3} x^{24}+\frac {5}{27} a \,b^{4} x^{27}+\frac {1}{30} b^{5} x^{30}\) | \(58\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 57, normalized size = 0.83 \begin {gather*} \frac {1}{30} \, b^{5} x^{30} + \frac {5}{27} \, a b^{4} x^{27} + \frac {5}{12} \, a^{2} b^{3} x^{24} + \frac {10}{21} \, a^{3} b^{2} x^{21} + \frac {5}{18} \, a^{4} b x^{18} + \frac {1}{15} \, a^{5} x^{15} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 57, normalized size = 0.83 \begin {gather*} \frac {1}{30} \, b^{5} x^{30} + \frac {5}{27} \, a b^{4} x^{27} + \frac {5}{12} \, a^{2} b^{3} x^{24} + \frac {10}{21} \, a^{3} b^{2} x^{21} + \frac {5}{18} \, a^{4} b x^{18} + \frac {1}{15} \, a^{5} x^{15} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 66, normalized size = 0.96 \begin {gather*} \frac {a^{5} x^{15}}{15} + \frac {5 a^{4} b x^{18}}{18} + \frac {10 a^{3} b^{2} x^{21}}{21} + \frac {5 a^{2} b^{3} x^{24}}{12} + \frac {5 a b^{4} x^{27}}{27} + \frac {b^{5} x^{30}}{30} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.82, size = 57, normalized size = 0.83 \begin {gather*} \frac {1}{30} \, b^{5} x^{30} + \frac {5}{27} \, a b^{4} x^{27} + \frac {5}{12} \, a^{2} b^{3} x^{24} + \frac {10}{21} \, a^{3} b^{2} x^{21} + \frac {5}{18} \, a^{4} b x^{18} + \frac {1}{15} \, a^{5} x^{15} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.02, size = 57, normalized size = 0.83 \begin {gather*} \frac {a^5\,x^{15}}{15}+\frac {5\,a^4\,b\,x^{18}}{18}+\frac {10\,a^3\,b^2\,x^{21}}{21}+\frac {5\,a^2\,b^3\,x^{24}}{12}+\frac {5\,a\,b^4\,x^{27}}{27}+\frac {b^5\,x^{30}}{30} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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