Optimal. Leaf size=39 \[ \frac {2}{3} a A x^{3/2}+\frac {2}{9} (A b+a B) x^{9/2}+\frac {2}{15} b B x^{15/2} \]
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Rubi [A]
time = 0.01, antiderivative size = 39, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {459}
\begin {gather*} \frac {2}{9} x^{9/2} (a B+A b)+\frac {2}{3} a A x^{3/2}+\frac {2}{15} b B x^{15/2} \end {gather*}
Antiderivative was successfully verified.
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Rule 459
Rubi steps
\begin {align*} \int \sqrt {x} \left (a+b x^3\right ) \left (A+B x^3\right ) \, dx &=\int \left (a A \sqrt {x}+(A b+a B) x^{7/2}+b B x^{13/2}\right ) \, dx\\ &=\frac {2}{3} a A x^{3/2}+\frac {2}{9} (A b+a B) x^{9/2}+\frac {2}{15} b B x^{15/2}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 35, normalized size = 0.90 \begin {gather*} \frac {2}{45} x^{3/2} \left (15 a A+5 A b x^3+5 a B x^3+3 b B x^6\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 28, normalized size = 0.72
method | result | size |
derivativedivides | \(\frac {2 a A \,x^{\frac {3}{2}}}{3}+\frac {2 \left (A b +B a \right ) x^{\frac {9}{2}}}{9}+\frac {2 b B \,x^{\frac {15}{2}}}{15}\) | \(28\) |
default | \(\frac {2 a A \,x^{\frac {3}{2}}}{3}+\frac {2 \left (A b +B a \right ) x^{\frac {9}{2}}}{9}+\frac {2 b B \,x^{\frac {15}{2}}}{15}\) | \(28\) |
gosper | \(\frac {2 x^{\frac {3}{2}} \left (3 b B \,x^{6}+5 A b \,x^{3}+5 B a \,x^{3}+15 A a \right )}{45}\) | \(32\) |
trager | \(\frac {2 x^{\frac {3}{2}} \left (3 b B \,x^{6}+5 A b \,x^{3}+5 B a \,x^{3}+15 A a \right )}{45}\) | \(32\) |
risch | \(\frac {2 x^{\frac {3}{2}} \left (3 b B \,x^{6}+5 A b \,x^{3}+5 B a \,x^{3}+15 A a \right )}{45}\) | \(32\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 27, normalized size = 0.69 \begin {gather*} \frac {2}{15} \, B b x^{\frac {15}{2}} + \frac {2}{9} \, {\left (B a + A b\right )} x^{\frac {9}{2}} + \frac {2}{3} \, A a x^{\frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 2.18, size = 30, normalized size = 0.77 \begin {gather*} \frac {2}{45} \, {\left (3 \, B b x^{7} + 5 \, {\left (B a + A b\right )} x^{4} + 15 \, A a x\right )} \sqrt {x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 1.22, size = 46, normalized size = 1.18 \begin {gather*} \frac {2 A a x^{\frac {3}{2}}}{3} + \frac {2 A b x^{\frac {9}{2}}}{9} + \frac {2 B a x^{\frac {9}{2}}}{9} + \frac {2 B b x^{\frac {15}{2}}}{15} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.58, size = 29, normalized size = 0.74 \begin {gather*} \frac {2}{15} \, B b x^{\frac {15}{2}} + \frac {2}{9} \, B a x^{\frac {9}{2}} + \frac {2}{9} \, A b x^{\frac {9}{2}} + \frac {2}{3} \, A a x^{\frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 31, normalized size = 0.79 \begin {gather*} \frac {2\,x^{3/2}\,\left (15\,A\,a+5\,A\,b\,x^3+5\,B\,a\,x^3+3\,B\,b\,x^6\right )}{45} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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