Optimal. Leaf size=43 \[ \frac {a^3 x^3}{3}+\frac {3}{7} a^2 b x^7+\frac {3}{11} a b^2 x^{11}+\frac {b^3 x^{15}}{15} \]
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Rubi [A]
time = 0.01, antiderivative size = 43, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {276}
\begin {gather*} \frac {a^3 x^3}{3}+\frac {3}{7} a^2 b x^7+\frac {3}{11} a b^2 x^{11}+\frac {b^3 x^{15}}{15} \end {gather*}
Antiderivative was successfully verified.
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Rule 276
Rubi steps
\begin {align*} \int x^2 \left (a+b x^4\right )^3 \, dx &=\int \left (a^3 x^2+3 a^2 b x^6+3 a b^2 x^{10}+b^3 x^{14}\right ) \, dx\\ &=\frac {a^3 x^3}{3}+\frac {3}{7} a^2 b x^7+\frac {3}{11} a b^2 x^{11}+\frac {b^3 x^{15}}{15}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 43, normalized size = 1.00 \begin {gather*} \frac {a^3 x^3}{3}+\frac {3}{7} a^2 b x^7+\frac {3}{11} a b^2 x^{11}+\frac {b^3 x^{15}}{15} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.14, size = 36, normalized size = 0.84
method | result | size |
gosper | \(\frac {1}{3} a^{3} x^{3}+\frac {3}{7} a^{2} b \,x^{7}+\frac {3}{11} a \,b^{2} x^{11}+\frac {1}{15} b^{3} x^{15}\) | \(36\) |
default | \(\frac {1}{3} a^{3} x^{3}+\frac {3}{7} a^{2} b \,x^{7}+\frac {3}{11} a \,b^{2} x^{11}+\frac {1}{15} b^{3} x^{15}\) | \(36\) |
norman | \(\frac {1}{3} a^{3} x^{3}+\frac {3}{7} a^{2} b \,x^{7}+\frac {3}{11} a \,b^{2} x^{11}+\frac {1}{15} b^{3} x^{15}\) | \(36\) |
risch | \(\frac {1}{3} a^{3} x^{3}+\frac {3}{7} a^{2} b \,x^{7}+\frac {3}{11} a \,b^{2} x^{11}+\frac {1}{15} b^{3} x^{15}\) | \(36\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 35, normalized size = 0.81 \begin {gather*} \frac {1}{15} \, b^{3} x^{15} + \frac {3}{11} \, a b^{2} x^{11} + \frac {3}{7} \, a^{2} b x^{7} + \frac {1}{3} \, a^{3} x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 35, normalized size = 0.81 \begin {gather*} \frac {1}{15} \, b^{3} x^{15} + \frac {3}{11} \, a b^{2} x^{11} + \frac {3}{7} \, a^{2} b x^{7} + \frac {1}{3} \, a^{3} x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 39, normalized size = 0.91 \begin {gather*} \frac {a^{3} x^{3}}{3} + \frac {3 a^{2} b x^{7}}{7} + \frac {3 a b^{2} x^{11}}{11} + \frac {b^{3} x^{15}}{15} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.59, size = 35, normalized size = 0.81 \begin {gather*} \frac {1}{15} \, b^{3} x^{15} + \frac {3}{11} \, a b^{2} x^{11} + \frac {3}{7} \, a^{2} b x^{7} + \frac {1}{3} \, a^{3} x^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 35, normalized size = 0.81 \begin {gather*} \frac {a^3\,x^3}{3}+\frac {3\,a^2\,b\,x^7}{7}+\frac {3\,a\,b^2\,x^{11}}{11}+\frac {b^3\,x^{15}}{15} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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