Optimal. Leaf size=72 \[ \frac {a^5 x^3}{3}+\frac {10}{7} a^4 b x^{7/2}+\frac {5}{2} a^3 b^2 x^4+\frac {20}{9} a^2 b^3 x^{9/2}+a b^4 x^5+\frac {2}{11} b^5 x^{11/2} \]
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Rubi [A] time = 0.04, antiderivative size = 72, 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} \[ \frac {20}{9} a^2 b^3 x^{9/2}+\frac {5}{2} a^3 b^2 x^4+\frac {10}{7} a^4 b x^{7/2}+\frac {a^5 x^3}{3}+a b^4 x^5+\frac {2}{11} b^5 x^{11/2} \]
Antiderivative was successfully verified.
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Rule 43
Rule 266
Rubi steps
\begin {align*} \int \left (a+b \sqrt {x}\right )^5 x^2 \, dx &=2 \operatorname {Subst}\left (\int x^5 (a+b x)^5 \, dx,x,\sqrt {x}\right )\\ &=2 \operatorname {Subst}\left (\int \left (a^5 x^5+5 a^4 b x^6+10 a^3 b^2 x^7+10 a^2 b^3 x^8+5 a b^4 x^9+b^5 x^{10}\right ) \, dx,x,\sqrt {x}\right )\\ &=\frac {a^5 x^3}{3}+\frac {10}{7} a^4 b x^{7/2}+\frac {5}{2} a^3 b^2 x^4+\frac {20}{9} a^2 b^3 x^{9/2}+a b^4 x^5+\frac {2}{11} b^5 x^{11/2}\\ \end {align*}
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Mathematica [A] time = 0.03, size = 72, normalized size = 1.00 \[ \frac {a^5 x^3}{3}+\frac {10}{7} a^4 b x^{7/2}+\frac {5}{2} a^3 b^2 x^4+\frac {20}{9} a^2 b^3 x^{9/2}+a b^4 x^5+\frac {2}{11} b^5 x^{11/2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.97, size = 62, normalized size = 0.86 \[ a b^{4} x^{5} + \frac {5}{2} \, a^{3} b^{2} x^{4} + \frac {1}{3} \, a^{5} x^{3} + \frac {2}{693} \, {\left (63 \, b^{5} x^{5} + 770 \, a^{2} b^{3} x^{4} + 495 \, a^{4} b x^{3}\right )} \sqrt {x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 56, normalized size = 0.78 \[ \frac {2}{11} \, b^{5} x^{\frac {11}{2}} + a b^{4} x^{5} + \frac {20}{9} \, a^{2} b^{3} x^{\frac {9}{2}} + \frac {5}{2} \, a^{3} b^{2} x^{4} + \frac {10}{7} \, a^{4} b x^{\frac {7}{2}} + \frac {1}{3} \, a^{5} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 57, normalized size = 0.79 \[ \frac {2 b^{5} x^{\frac {11}{2}}}{11}+a \,b^{4} x^{5}+\frac {20 a^{2} b^{3} x^{\frac {9}{2}}}{9}+\frac {5 a^{3} b^{2} x^{4}}{2}+\frac {10 a^{4} b \,x^{\frac {7}{2}}}{7}+\frac {a^{5} x^{3}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.90, size = 98, normalized size = 1.36 \[ \frac {2 \, {\left (b \sqrt {x} + a\right )}^{11}}{11 \, b^{6}} - \frac {{\left (b \sqrt {x} + a\right )}^{10} a}{b^{6}} + \frac {20 \, {\left (b \sqrt {x} + a\right )}^{9} a^{2}}{9 \, b^{6}} - \frac {5 \, {\left (b \sqrt {x} + a\right )}^{8} a^{3}}{2 \, b^{6}} + \frac {10 \, {\left (b \sqrt {x} + a\right )}^{7} a^{4}}{7 \, b^{6}} - \frac {{\left (b \sqrt {x} + a\right )}^{6} a^{5}}{3 \, b^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 56, normalized size = 0.78 \[ \frac {a^5\,x^3}{3}+\frac {2\,b^5\,x^{11/2}}{11}+a\,b^4\,x^5+\frac {10\,a^4\,b\,x^{7/2}}{7}+\frac {5\,a^3\,b^2\,x^4}{2}+\frac {20\,a^2\,b^3\,x^{9/2}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 2.34, size = 70, normalized size = 0.97 \[ \frac {a^{5} x^{3}}{3} + \frac {10 a^{4} b x^{\frac {7}{2}}}{7} + \frac {5 a^{3} b^{2} x^{4}}{2} + \frac {20 a^{2} b^{3} x^{\frac {9}{2}}}{9} + a b^{4} x^{5} + \frac {2 b^{5} x^{\frac {11}{2}}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
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