Optimal. Leaf size=32 \[ \frac {a^2 x^5}{5}+\frac {4}{11} a b x^{11/2}+\frac {b^2 x^6}{6} \]
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Rubi [A] time = 0.03, antiderivative size = 32, 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} \[ \frac {a^2 x^5}{5}+\frac {4}{11} a b x^{11/2}+\frac {b^2 x^6}{6} \]
Antiderivative was successfully verified.
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Rule 43
Rule 266
Rubi steps
\begin {align*} \int \left (a+b \sqrt {x}\right )^2 x^4 \, dx &=2 \operatorname {Subst}\left (\int x^9 (a+b x)^2 \, dx,x,\sqrt {x}\right )\\ &=2 \operatorname {Subst}\left (\int \left (a^2 x^9+2 a b x^{10}+b^2 x^{11}\right ) \, dx,x,\sqrt {x}\right )\\ &=\frac {a^2 x^5}{5}+\frac {4}{11} a b x^{11/2}+\frac {b^2 x^6}{6}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 28, normalized size = 0.88 \[ \frac {1}{330} x^5 \left (66 a^2+120 a b \sqrt {x}+55 b^2 x\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.87, size = 24, normalized size = 0.75 \[ \frac {1}{6} \, b^{2} x^{6} + \frac {4}{11} \, a b x^{\frac {11}{2}} + \frac {1}{5} \, a^{2} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 24, normalized size = 0.75 \[ \frac {1}{6} \, b^{2} x^{6} + \frac {4}{11} \, a b x^{\frac {11}{2}} + \frac {1}{5} \, a^{2} x^{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 25, normalized size = 0.78 \[ \frac {b^{2} x^{6}}{6}+\frac {4 a b \,x^{\frac {11}{2}}}{11}+\frac {a^{2} x^{5}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.85, size = 166, normalized size = 5.19 \[ \frac {{\left (b \sqrt {x} + a\right )}^{12}}{6 \, b^{10}} - \frac {18 \, {\left (b \sqrt {x} + a\right )}^{11} a}{11 \, b^{10}} + \frac {36 \, {\left (b \sqrt {x} + a\right )}^{10} a^{2}}{5 \, b^{10}} - \frac {56 \, {\left (b \sqrt {x} + a\right )}^{9} a^{3}}{3 \, b^{10}} + \frac {63 \, {\left (b \sqrt {x} + a\right )}^{8} a^{4}}{2 \, b^{10}} - \frac {36 \, {\left (b \sqrt {x} + a\right )}^{7} a^{5}}{b^{10}} + \frac {28 \, {\left (b \sqrt {x} + a\right )}^{6} a^{6}}{b^{10}} - \frac {72 \, {\left (b \sqrt {x} + a\right )}^{5} a^{7}}{5 \, b^{10}} + \frac {9 \, {\left (b \sqrt {x} + a\right )}^{4} a^{8}}{2 \, b^{10}} - \frac {2 \, {\left (b \sqrt {x} + a\right )}^{3} a^{9}}{3 \, b^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.10, size = 24, normalized size = 0.75 \[ \frac {a^2\,x^5}{5}+\frac {b^2\,x^6}{6}+\frac {4\,a\,b\,x^{11/2}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.46, size = 27, normalized size = 0.84 \[ \frac {a^{2} x^{5}}{5} + \frac {4 a b x^{\frac {11}{2}}}{11} + \frac {b^{2} x^{6}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
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