Optimal. Leaf size=16 \[ \frac {\left (a+b x^2\right )^6}{12 b} \]
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Rubi [A] time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {261} \[ \frac {\left (a+b x^2\right )^6}{12 b} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin {align*} \int x \left (a+b x^2\right )^5 \, dx &=\frac {\left (a+b x^2\right )^6}{12 b}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 1.00 \[ \frac {\left (a+b x^2\right )^6}{12 b} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.77, size = 57, normalized size = 3.56 \[ \frac {1}{12} x^{12} b^{5} + \frac {1}{2} x^{10} b^{4} a + \frac {5}{4} x^{8} b^{3} a^{2} + \frac {5}{3} x^{6} b^{2} a^{3} + \frac {5}{4} x^{4} b a^{4} + \frac {1}{2} x^{2} a^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.06, size = 14, normalized size = 0.88 \[ \frac {{\left (b x^{2} + a\right )}^{6}}{12 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.00, size = 58, normalized size = 3.62 \[ \frac {1}{12} b^{5} x^{12}+\frac {1}{2} a \,b^{4} x^{10}+\frac {5}{4} a^{2} b^{3} x^{8}+\frac {5}{3} a^{3} b^{2} x^{6}+\frac {5}{4} a^{4} b \,x^{4}+\frac {1}{2} a^{5} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.40, size = 14, normalized size = 0.88 \[ \frac {{\left (b x^{2} + a\right )}^{6}}{12 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 57, normalized size = 3.56 \[ \frac {a^5\,x^2}{2}+\frac {5\,a^4\,b\,x^4}{4}+\frac {5\,a^3\,b^2\,x^6}{3}+\frac {5\,a^2\,b^3\,x^8}{4}+\frac {a\,b^4\,x^{10}}{2}+\frac {b^5\,x^{12}}{12} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.08, size = 65, normalized size = 4.06 \[ \frac {a^{5} x^{2}}{2} + \frac {5 a^{4} b x^{4}}{4} + \frac {5 a^{3} b^{2} x^{6}}{3} + \frac {5 a^{2} b^{3} x^{8}}{4} + \frac {a b^{4} x^{10}}{2} + \frac {b^{5} x^{12}}{12} \]
Verification of antiderivative is not currently implemented for this CAS.
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