Optimal. Leaf size=47 \[ \frac {a^3 x^5}{5}+\frac {6}{11} a^2 b x^{11/2}+\frac {1}{2} a b^2 x^6+\frac {2}{13} b^3 x^{13/2} \]
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Rubi [A] time = 0.03, antiderivative size = 47, 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 = {266, 43} \[ \frac {6}{11} a^2 b x^{11/2}+\frac {a^3 x^5}{5}+\frac {1}{2} a b^2 x^6+\frac {2}{13} b^3 x^{13/2} \]
Antiderivative was successfully verified.
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Rule 43
Rule 266
Rubi steps
\begin {align*} \int \left (a+b \sqrt {x}\right )^3 x^4 \, dx &=2 \operatorname {Subst}\left (\int x^9 (a+b x)^3 \, dx,x,\sqrt {x}\right )\\ &=2 \operatorname {Subst}\left (\int \left (a^3 x^9+3 a^2 b x^{10}+3 a b^2 x^{11}+b^3 x^{12}\right ) \, dx,x,\sqrt {x}\right )\\ &=\frac {a^3 x^5}{5}+\frac {6}{11} a^2 b x^{11/2}+\frac {1}{2} a b^2 x^6+\frac {2}{13} b^3 x^{13/2}\\ \end {align*}
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Mathematica [A] time = 0.05, size = 47, normalized size = 1.00 \[ \frac {a^3 x^5}{5}+\frac {6}{11} a^2 b x^{11/2}+\frac {1}{2} a b^2 x^6+\frac {2}{13} b^3 x^{13/2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.93, size = 41, normalized size = 0.87 \[ \frac {1}{2} \, a b^{2} x^{6} + \frac {1}{5} \, a^{3} x^{5} + \frac {2}{143} \, {\left (11 \, b^{3} x^{6} + 39 \, a^{2} b x^{5}\right )} \sqrt {x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 35, normalized size = 0.74 \[ \frac {2}{13} \, b^{3} x^{\frac {13}{2}} + \frac {1}{2} \, a b^{2} x^{6} + \frac {6}{11} \, a^{2} b x^{\frac {11}{2}} + \frac {1}{5} \, a^{3} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 36, normalized size = 0.77 \[ \frac {2 b^{3} x^{\frac {13}{2}}}{13}+\frac {a \,b^{2} x^{6}}{2}+\frac {6 a^{2} b \,x^{\frac {11}{2}}}{11}+\frac {a^{3} x^{5}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.92, size = 166, normalized size = 3.53 \[ \frac {2 \, {\left (b \sqrt {x} + a\right )}^{13}}{13 \, b^{10}} - \frac {3 \, {\left (b \sqrt {x} + a\right )}^{12} a}{2 \, b^{10}} + \frac {72 \, {\left (b \sqrt {x} + a\right )}^{11} a^{2}}{11 \, b^{10}} - \frac {84 \, {\left (b \sqrt {x} + a\right )}^{10} a^{3}}{5 \, b^{10}} + \frac {28 \, {\left (b \sqrt {x} + a\right )}^{9} a^{4}}{b^{10}} - \frac {63 \, {\left (b \sqrt {x} + a\right )}^{8} a^{5}}{2 \, b^{10}} + \frac {24 \, {\left (b \sqrt {x} + a\right )}^{7} a^{6}}{b^{10}} - \frac {12 \, {\left (b \sqrt {x} + a\right )}^{6} a^{7}}{b^{10}} + \frac {18 \, {\left (b \sqrt {x} + a\right )}^{5} a^{8}}{5 \, b^{10}} - \frac {{\left (b \sqrt {x} + a\right )}^{4} a^{9}}{2 \, b^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 35, normalized size = 0.74 \[ \frac {a^3\,x^5}{5}+\frac {2\,b^3\,x^{13/2}}{13}+\frac {a\,b^2\,x^6}{2}+\frac {6\,a^2\,b\,x^{11/2}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 2.09, size = 42, normalized size = 0.89 \[ \frac {a^{3} x^{5}}{5} + \frac {6 a^{2} b x^{\frac {11}{2}}}{11} + \frac {a b^{2} x^{6}}{2} + \frac {2 b^{3} x^{\frac {13}{2}}}{13} \]
Verification of antiderivative is not currently implemented for this CAS.
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