Optimal. Leaf size=44 \[ \frac {a^3 x^2}{2}+\frac {6}{5} a^2 b x^{5/2}+a b^2 x^3+\frac {2}{7} b^3 x^{7/2} \]
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Rubi [A] time = 0.02, antiderivative size = 44, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {266, 43} \[ \frac {6}{5} a^2 b x^{5/2}+\frac {a^3 x^2}{2}+a b^2 x^3+\frac {2}{7} b^3 x^{7/2} \]
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 \, dx &=2 \operatorname {Subst}\left (\int x^3 (a+b x)^3 \, dx,x,\sqrt {x}\right )\\ &=2 \operatorname {Subst}\left (\int \left (a^3 x^3+3 a^2 b x^4+3 a b^2 x^5+b^3 x^6\right ) \, dx,x,\sqrt {x}\right )\\ &=\frac {a^3 x^2}{2}+\frac {6}{5} a^2 b x^{5/2}+a b^2 x^3+\frac {2}{7} b^3 x^{7/2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 44, normalized size = 1.00 \[ \frac {a^3 x^2}{2}+\frac {6}{5} a^2 b x^{5/2}+a b^2 x^3+\frac {2}{7} b^3 x^{7/2} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.15, size = 40, normalized size = 0.91 \[ a b^{2} x^{3} + \frac {1}{2} \, a^{3} x^{2} + \frac {2}{35} \, {\left (5 \, b^{3} x^{3} + 21 \, a^{2} b x^{2}\right )} \sqrt {x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 34, normalized size = 0.77 \[ \frac {2}{7} \, b^{3} x^{\frac {7}{2}} + a b^{2} x^{3} + \frac {6}{5} \, a^{2} b x^{\frac {5}{2}} + \frac {1}{2} \, a^{3} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 35, normalized size = 0.80 \[ \frac {2 b^{3} x^{\frac {7}{2}}}{7}+a \,b^{2} x^{3}+\frac {6 a^{2} b \,x^{\frac {5}{2}}}{5}+\frac {a^{3} x^{2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.84, size = 64, normalized size = 1.45 \[ \frac {2 \, {\left (b \sqrt {x} + a\right )}^{7}}{7 \, b^{4}} - \frac {{\left (b \sqrt {x} + a\right )}^{6} a}{b^{4}} + \frac {6 \, {\left (b \sqrt {x} + a\right )}^{5} a^{2}}{5 \, b^{4}} - \frac {{\left (b \sqrt {x} + a\right )}^{4} a^{3}}{2 \, b^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 34, normalized size = 0.77 \[ \frac {a^3\,x^2}{2}+\frac {2\,b^3\,x^{7/2}}{7}+a\,b^2\,x^3+\frac {6\,a^2\,b\,x^{5/2}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.86, size = 41, normalized size = 0.93 \[ \frac {a^{3} x^{2}}{2} + \frac {6 a^{2} b x^{\frac {5}{2}}}{5} + a b^{2} x^{3} + \frac {2 b^{3} x^{\frac {7}{2}}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
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