Optimal. Leaf size=30 \[ \frac {a^2 x^6}{6}+\frac {2}{7} a b x^7+\frac {b^2 x^8}{8} \]
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Rubi [A]
time = 0.01, antiderivative size = 30, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {1598, 45}
\begin {gather*} \frac {a^2 x^6}{6}+\frac {2}{7} a b x^7+\frac {b^2 x^8}{8} \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rule 1598
Rubi steps
\begin {align*} \int x \left (a x^2+b x^3\right )^2 \, dx &=\int x^5 (a+b x)^2 \, dx\\ &=\int \left (a^2 x^5+2 a b x^6+b^2 x^7\right ) \, dx\\ &=\frac {a^2 x^6}{6}+\frac {2}{7} a b x^7+\frac {b^2 x^8}{8}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 30, normalized size = 1.00 \begin {gather*} \frac {a^2 x^6}{6}+\frac {2}{7} a b x^7+\frac {b^2 x^8}{8} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.34, size = 25, normalized size = 0.83
method | result | size |
gosper | \(\frac {x^{6} \left (21 b^{2} x^{2}+48 a b x +28 a^{2}\right )}{168}\) | \(25\) |
default | \(\frac {1}{6} a^{2} x^{6}+\frac {2}{7} a b \,x^{7}+\frac {1}{8} b^{2} x^{8}\) | \(25\) |
norman | \(\frac {1}{6} a^{2} x^{6}+\frac {2}{7} a b \,x^{7}+\frac {1}{8} b^{2} x^{8}\) | \(25\) |
risch | \(\frac {1}{6} a^{2} x^{6}+\frac {2}{7} a b \,x^{7}+\frac {1}{8} b^{2} x^{8}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 24, normalized size = 0.80 \begin {gather*} \frac {1}{8} \, b^{2} x^{8} + \frac {2}{7} \, a b x^{7} + \frac {1}{6} \, a^{2} x^{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.14, size = 24, normalized size = 0.80 \begin {gather*} \frac {1}{8} \, b^{2} x^{8} + \frac {2}{7} \, a b x^{7} + \frac {1}{6} \, a^{2} x^{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 26, normalized size = 0.87 \begin {gather*} \frac {a^{2} x^{6}}{6} + \frac {2 a b x^{7}}{7} + \frac {b^{2} x^{8}}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.44, size = 24, normalized size = 0.80 \begin {gather*} \frac {1}{8} \, b^{2} x^{8} + \frac {2}{7} \, a b x^{7} + \frac {1}{6} \, a^{2} x^{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 24, normalized size = 0.80 \begin {gather*} \frac {a^2\,x^6}{6}+\frac {2\,a\,b\,x^7}{7}+\frac {b^2\,x^8}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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