Optimal. Leaf size=38 \[ a^3 x+\frac {3}{5} a^2 b x^5+\frac {1}{3} a b^2 x^9+\frac {b^3 x^{13}}{13} \]
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Rubi [A]
time = 0.01, antiderivative size = 38, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {200}
\begin {gather*} a^3 x+\frac {3}{5} a^2 b x^5+\frac {1}{3} a b^2 x^9+\frac {b^3 x^{13}}{13} \end {gather*}
Antiderivative was successfully verified.
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Rule 200
Rubi steps
\begin {align*} \int \left (a+b x^4\right )^3 \, dx &=\int \left (a^3+3 a^2 b x^4+3 a b^2 x^8+b^3 x^{12}\right ) \, dx\\ &=a^3 x+\frac {3}{5} a^2 b x^5+\frac {1}{3} a b^2 x^9+\frac {b^3 x^{13}}{13}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 38, normalized size = 1.00 \begin {gather*} a^3 x+\frac {3}{5} a^2 b x^5+\frac {1}{3} a b^2 x^9+\frac {b^3 x^{13}}{13} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 33, normalized size = 0.87
method | result | size |
gosper | \(a^{3} x +\frac {3}{5} a^{2} b \,x^{5}+\frac {1}{3} a \,b^{2} x^{9}+\frac {1}{13} b^{3} x^{13}\) | \(33\) |
default | \(a^{3} x +\frac {3}{5} a^{2} b \,x^{5}+\frac {1}{3} a \,b^{2} x^{9}+\frac {1}{13} b^{3} x^{13}\) | \(33\) |
norman | \(a^{3} x +\frac {3}{5} a^{2} b \,x^{5}+\frac {1}{3} a \,b^{2} x^{9}+\frac {1}{13} b^{3} x^{13}\) | \(33\) |
risch | \(a^{3} x +\frac {3}{5} a^{2} b \,x^{5}+\frac {1}{3} a \,b^{2} x^{9}+\frac {1}{13} b^{3} x^{13}\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 32, normalized size = 0.84 \begin {gather*} \frac {1}{13} \, b^{3} x^{13} + \frac {1}{3} \, a b^{2} x^{9} + \frac {3}{5} \, a^{2} b x^{5} + a^{3} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 32, normalized size = 0.84 \begin {gather*} \frac {1}{13} \, b^{3} x^{13} + \frac {1}{3} \, a b^{2} x^{9} + \frac {3}{5} \, a^{2} b x^{5} + a^{3} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 34, normalized size = 0.89 \begin {gather*} a^{3} x + \frac {3 a^{2} b x^{5}}{5} + \frac {a b^{2} x^{9}}{3} + \frac {b^{3} x^{13}}{13} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.51, size = 32, normalized size = 0.84 \begin {gather*} \frac {1}{13} \, b^{3} x^{13} + \frac {1}{3} \, a b^{2} x^{9} + \frac {3}{5} \, a^{2} b x^{5} + a^{3} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 32, normalized size = 0.84 \begin {gather*} a^3\,x+\frac {3\,a^2\,b\,x^5}{5}+\frac {a\,b^2\,x^9}{3}+\frac {b^3\,x^{13}}{13} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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