Optimal. Leaf size=47 \[ \frac {a^3 x^4}{4}+\frac {2}{3} a^2 b x^{9/2}+\frac {3}{5} a b^2 x^5+\frac {2}{11} b^3 x^{11/2} \]
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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} \[ \frac {2}{3} a^2 b x^{9/2}+\frac {a^3 x^4}{4}+\frac {3}{5} a b^2 x^5+\frac {2}{11} b^3 x^{11/2} \]
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^3 \, dx &=2 \operatorname {Subst}\left (\int x^7 (a+b x)^3 \, dx,x,\sqrt {x}\right )\\ &=2 \operatorname {Subst}\left (\int \left (a^3 x^7+3 a^2 b x^8+3 a b^2 x^9+b^3 x^{10}\right ) \, dx,x,\sqrt {x}\right )\\ &=\frac {a^3 x^4}{4}+\frac {2}{3} a^2 b x^{9/2}+\frac {3}{5} a b^2 x^5+\frac {2}{11} b^3 x^{11/2}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 47, normalized size = 1.00 \[ \frac {a^3 x^4}{4}+\frac {2}{3} a^2 b x^{9/2}+\frac {3}{5} a b^2 x^5+\frac {2}{11} b^3 x^{11/2} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.00, size = 41, normalized size = 0.87 \[ \frac {3}{5} \, a b^{2} x^{5} + \frac {1}{4} \, a^{3} x^{4} + \frac {2}{33} \, {\left (3 \, b^{3} x^{5} + 11 \, a^{2} b x^{4}\right )} \sqrt {x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 35, normalized size = 0.74 \[ \frac {2}{11} \, b^{3} x^{\frac {11}{2}} + \frac {3}{5} \, a b^{2} x^{5} + \frac {2}{3} \, a^{2} b x^{\frac {9}{2}} + \frac {1}{4} \, a^{3} x^{4} \]
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 \[ \frac {2 b^{3} x^{\frac {11}{2}}}{11}+\frac {3 a \,b^{2} x^{5}}{5}+\frac {2 a^{2} b \,x^{\frac {9}{2}}}{3}+\frac {a^{3} x^{4}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.94, size = 132, normalized size = 2.81 \[ \frac {2 \, {\left (b \sqrt {x} + a\right )}^{11}}{11 \, b^{8}} - \frac {7 \, {\left (b \sqrt {x} + a\right )}^{10} a}{5 \, b^{8}} + \frac {14 \, {\left (b \sqrt {x} + a\right )}^{9} a^{2}}{3 \, b^{8}} - \frac {35 \, {\left (b \sqrt {x} + a\right )}^{8} a^{3}}{4 \, b^{8}} + \frac {10 \, {\left (b \sqrt {x} + a\right )}^{7} a^{4}}{b^{8}} - \frac {7 \, {\left (b \sqrt {x} + a\right )}^{6} a^{5}}{b^{8}} + \frac {14 \, {\left (b \sqrt {x} + a\right )}^{5} a^{6}}{5 \, b^{8}} - \frac {{\left (b \sqrt {x} + a\right )}^{4} a^{7}}{2 \, b^{8}} \]
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 \[ \frac {a^3\,x^4}{4}+\frac {2\,b^3\,x^{11/2}}{11}+\frac {3\,a\,b^2\,x^5}{5}+\frac {2\,a^2\,b\,x^{9/2}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.92, size = 44, normalized size = 0.94 \[ \frac {a^{3} x^{4}}{4} + \frac {2 a^{2} b x^{\frac {9}{2}}}{3} + \frac {3 a b^{2} x^{5}}{5} + \frac {2 b^{3} x^{\frac {11}{2}}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
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