Optimal. Leaf size=55 \[ \frac {1}{2} a^2 A x^2+\frac {1}{5} a (2 A b+a B) x^5+\frac {1}{8} b (A b+2 a B) x^8+\frac {1}{11} b^2 B x^{11} \]
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Rubi [A]
time = 0.02, antiderivative size = 55, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {459}
\begin {gather*} \frac {1}{2} a^2 A x^2+\frac {1}{8} b x^8 (2 a B+A b)+\frac {1}{5} a x^5 (a B+2 A b)+\frac {1}{11} b^2 B x^{11} \end {gather*}
Antiderivative was successfully verified.
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Rule 459
Rubi steps
\begin {align*} \int x \left (a+b x^3\right )^2 \left (A+B x^3\right ) \, dx &=\int \left (a^2 A x+a (2 A b+a B) x^4+b (A b+2 a B) x^7+b^2 B x^{10}\right ) \, dx\\ &=\frac {1}{2} a^2 A x^2+\frac {1}{5} a (2 A b+a B) x^5+\frac {1}{8} b (A b+2 a B) x^8+\frac {1}{11} b^2 B x^{11}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 55, normalized size = 1.00 \begin {gather*} \frac {1}{2} a^2 A x^2+\frac {1}{5} a (2 A b+a B) x^5+\frac {1}{8} b (A b+2 a B) x^8+\frac {1}{11} b^2 B x^{11} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.31, size = 52, normalized size = 0.95
method | result | size |
default | \(\frac {b^{2} B \,x^{11}}{11}+\frac {\left (b^{2} A +2 a b B \right ) x^{8}}{8}+\frac {\left (2 a b A +a^{2} B \right ) x^{5}}{5}+\frac {a^{2} A \,x^{2}}{2}\) | \(52\) |
norman | \(\frac {b^{2} B \,x^{11}}{11}+\left (\frac {1}{8} b^{2} A +\frac {1}{4} a b B \right ) x^{8}+\left (\frac {2}{5} a b A +\frac {1}{5} a^{2} B \right ) x^{5}+\frac {a^{2} A \,x^{2}}{2}\) | \(52\) |
gosper | \(\frac {1}{11} b^{2} B \,x^{11}+\frac {1}{8} x^{8} b^{2} A +\frac {1}{4} x^{8} a b B +\frac {2}{5} x^{5} a b A +\frac {1}{5} a^{2} B \,x^{5}+\frac {1}{2} a^{2} A \,x^{2}\) | \(54\) |
risch | \(\frac {1}{11} b^{2} B \,x^{11}+\frac {1}{8} x^{8} b^{2} A +\frac {1}{4} x^{8} a b B +\frac {2}{5} x^{5} a b A +\frac {1}{5} a^{2} B \,x^{5}+\frac {1}{2} a^{2} A \,x^{2}\) | \(54\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 51, normalized size = 0.93 \begin {gather*} \frac {1}{11} \, B b^{2} x^{11} + \frac {1}{8} \, {\left (2 \, B a b + A b^{2}\right )} x^{8} + \frac {1}{5} \, {\left (B a^{2} + 2 \, A a b\right )} x^{5} + \frac {1}{2} \, A a^{2} x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 2.01, size = 51, normalized size = 0.93 \begin {gather*} \frac {1}{11} \, B b^{2} x^{11} + \frac {1}{8} \, {\left (2 \, B a b + A b^{2}\right )} x^{8} + \frac {1}{5} \, {\left (B a^{2} + 2 \, A a b\right )} x^{5} + \frac {1}{2} \, A a^{2} x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 54, normalized size = 0.98 \begin {gather*} \frac {A a^{2} x^{2}}{2} + \frac {B b^{2} x^{11}}{11} + x^{8} \left (\frac {A b^{2}}{8} + \frac {B a b}{4}\right ) + x^{5} \cdot \left (\frac {2 A a b}{5} + \frac {B a^{2}}{5}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.01, size = 53, normalized size = 0.96 \begin {gather*} \frac {1}{11} \, B b^{2} x^{11} + \frac {1}{4} \, B a b x^{8} + \frac {1}{8} \, A b^{2} x^{8} + \frac {1}{5} \, B a^{2} x^{5} + \frac {2}{5} \, A a b x^{5} + \frac {1}{2} \, A a^{2} x^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 51, normalized size = 0.93 \begin {gather*} x^5\,\left (\frac {B\,a^2}{5}+\frac {2\,A\,b\,a}{5}\right )+x^8\,\left (\frac {A\,b^2}{8}+\frac {B\,a\,b}{4}\right )+\frac {A\,a^2\,x^2}{2}+\frac {B\,b^2\,x^{11}}{11} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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