Optimal. Leaf size=31 \[ \frac {2}{3} \sqrt {\frac {7}{5}} E\left (\sin ^{-1}\left (\sqrt {5} \sqrt {2+3 x}\right )|\frac {2}{35}\right ) \]
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Rubi [A]
time = 0.01, antiderivative size = 31, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.036, Rules used = {114}
\begin {gather*} \frac {2}{3} \sqrt {\frac {7}{5}} E\left (\text {ArcSin}\left (\sqrt {5} \sqrt {3 x+2}\right )|\frac {2}{35}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 114
Rubi steps
\begin {align*} \int \frac {\sqrt {1-2 x}}{\sqrt {-3-5 x} \sqrt {2+3 x}} \, dx &=\frac {2}{3} \sqrt {\frac {7}{5}} E\left (\sin ^{-1}\left (\sqrt {5} \sqrt {2+3 x}\right )|\frac {2}{35}\right )\\ \end {align*}
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Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(109\) vs. \(2(31)=62\).
time = 1.38, size = 109, normalized size = 3.52 \begin {gather*} -\frac {2 \left (\frac {3 \left (-3+x+10 x^2\right )}{\sqrt {2+3 x}}+\sqrt {35} \sqrt {\frac {-1+2 x}{2+3 x}} (2+3 x) \sqrt {\frac {3+5 x}{2+3 x}} E\left (\sin ^{-1}\left (\frac {\sqrt {\frac {7}{2}}}{\sqrt {2+3 x}}\right )|\frac {2}{35}\right )\right )}{15 \sqrt {-3-5 x} \sqrt {1-2 x}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 41, normalized size = 1.32
method | result | size |
default | \(\frac {\left (33 \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )+2 \EllipticE \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )\right ) \sqrt {2}}{15}\) | \(41\) |
elliptic | \(\frac {\sqrt {\left (3+5 x \right ) \left (-1+2 x \right ) \left (2+3 x \right )}\, \left (\frac {\sqrt {28+42 x}\, \sqrt {-15 x -9}\, \sqrt {21-42 x}\, \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )}{21 \sqrt {30 x^{3}+23 x^{2}-7 x -6}}-\frac {2 \sqrt {28+42 x}\, \sqrt {-15 x -9}\, \sqrt {21-42 x}\, \left (-\frac {\EllipticE \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )}{15}-\frac {3 \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )}{5}\right )}{21 \sqrt {30 x^{3}+23 x^{2}-7 x -6}}\right )}{\sqrt {1-2 x}\, \sqrt {-3-5 x}\, \sqrt {2+3 x}}\) | \(172\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [C] Result contains higher order function than in optimal. Order 9 vs. order
4.
time = 0.13, size = 26, normalized size = 0.84 \begin {gather*} \frac {68}{675} \, \sqrt {30} {\rm weierstrassPInverse}\left (\frac {1159}{675}, \frac {38998}{91125}, x + \frac {23}{90}\right ) + \frac {2}{15} \, \sqrt {30} {\rm weierstrassZeta}\left (\frac {1159}{675}, \frac {38998}{91125}, {\rm weierstrassPInverse}\left (\frac {1159}{675}, \frac {38998}{91125}, x + \frac {23}{90}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\sqrt {1 - 2 x}}{\sqrt {- 5 x - 3} \sqrt {3 x + 2}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {\sqrt {1-2\,x}}{\sqrt {3\,x+2}\,\sqrt {-5\,x-3}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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