Optimal. Leaf size=66 \[ \frac {5929}{16 \sqrt {1-2 x}}+\frac {1309}{2} \sqrt {1-2 x}-\frac {3467}{24} (1-2 x)^{3/2}+\frac {51}{2} (1-2 x)^{5/2}-\frac {225}{112} (1-2 x)^{7/2} \]
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Rubi [A]
time = 0.01, antiderivative size = 66, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.042, Rules used = {90}
\begin {gather*} -\frac {225}{112} (1-2 x)^{7/2}+\frac {51}{2} (1-2 x)^{5/2}-\frac {3467}{24} (1-2 x)^{3/2}+\frac {1309}{2} \sqrt {1-2 x}+\frac {5929}{16 \sqrt {1-2 x}} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(2+3 x)^2 (3+5 x)^2}{(1-2 x)^{3/2}} \, dx &=\int \left (\frac {5929}{16 (1-2 x)^{3/2}}-\frac {1309}{2 \sqrt {1-2 x}}+\frac {3467}{8} \sqrt {1-2 x}-\frac {255}{2} (1-2 x)^{3/2}+\frac {225}{16} (1-2 x)^{5/2}\right ) \, dx\\ &=\frac {5929}{16 \sqrt {1-2 x}}+\frac {1309}{2} \sqrt {1-2 x}-\frac {3467}{24} (1-2 x)^{3/2}+\frac {51}{2} (1-2 x)^{5/2}-\frac {225}{112} (1-2 x)^{7/2}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 33, normalized size = 0.50 \begin {gather*} \frac {18986-18230 x-6721 x^2-2934 x^3-675 x^4}{21 \sqrt {1-2 x}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 47, normalized size = 0.71
method | result | size |
gosper | \(-\frac {675 x^{4}+2934 x^{3}+6721 x^{2}+18230 x -18986}{21 \sqrt {1-2 x}}\) | \(30\) |
risch | \(-\frac {675 x^{4}+2934 x^{3}+6721 x^{2}+18230 x -18986}{21 \sqrt {1-2 x}}\) | \(30\) |
trager | \(\frac {\left (675 x^{4}+2934 x^{3}+6721 x^{2}+18230 x -18986\right ) \sqrt {1-2 x}}{-21+42 x}\) | \(37\) |
derivativedivides | \(-\frac {3467 \left (1-2 x \right )^{\frac {3}{2}}}{24}+\frac {51 \left (1-2 x \right )^{\frac {5}{2}}}{2}-\frac {225 \left (1-2 x \right )^{\frac {7}{2}}}{112}+\frac {5929}{16 \sqrt {1-2 x}}+\frac {1309 \sqrt {1-2 x}}{2}\) | \(47\) |
default | \(-\frac {3467 \left (1-2 x \right )^{\frac {3}{2}}}{24}+\frac {51 \left (1-2 x \right )^{\frac {5}{2}}}{2}-\frac {225 \left (1-2 x \right )^{\frac {7}{2}}}{112}+\frac {5929}{16 \sqrt {1-2 x}}+\frac {1309 \sqrt {1-2 x}}{2}\) | \(47\) |
meijerg | \(-\frac {36 \left (\sqrt {\pi }-\frac {\sqrt {\pi }}{\sqrt {1-2 x}}\right )}{\sqrt {\pi }}+\frac {-228 \sqrt {\pi }+\frac {57 \sqrt {\pi }\, \left (-8 x +8\right )}{2 \sqrt {1-2 x}}}{\sqrt {\pi }}-\frac {541 \left (\frac {8 \sqrt {\pi }}{3}-\frac {\sqrt {\pi }\, \left (-8 x^{2}-16 x +16\right )}{6 \sqrt {1-2 x}}\right )}{4 \sqrt {\pi }}+\frac {-228 \sqrt {\pi }+\frac {57 \sqrt {\pi }\, \left (-64 x^{3}-64 x^{2}-128 x +128\right )}{32 \sqrt {1-2 x}}}{\sqrt {\pi }}-\frac {225 \left (\frac {128 \sqrt {\pi }}{35}-\frac {\sqrt {\pi }\, \left (-160 x^{4}-128 x^{3}-128 x^{2}-256 x +256\right )}{70 \sqrt {1-2 x}}\right )}{16 \sqrt {\pi }}\) | \(165\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 46, normalized size = 0.70 \begin {gather*} -\frac {225}{112} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} + \frac {51}{2} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} - \frac {3467}{24} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} + \frac {1309}{2} \, \sqrt {-2 \, x + 1} + \frac {5929}{16 \, \sqrt {-2 \, x + 1}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.80, size = 36, normalized size = 0.55 \begin {gather*} \frac {{\left (675 \, x^{4} + 2934 \, x^{3} + 6721 \, x^{2} + 18230 \, x - 18986\right )} \sqrt {-2 \, x + 1}}{21 \, {\left (2 \, x - 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 12.06, size = 58, normalized size = 0.88 \begin {gather*} - \frac {225 \left (1 - 2 x\right )^{\frac {7}{2}}}{112} + \frac {51 \left (1 - 2 x\right )^{\frac {5}{2}}}{2} - \frac {3467 \left (1 - 2 x\right )^{\frac {3}{2}}}{24} + \frac {1309 \sqrt {1 - 2 x}}{2} + \frac {5929}{16 \sqrt {1 - 2 x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.27, size = 60, normalized size = 0.91 \begin {gather*} \frac {225}{112} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} + \frac {51}{2} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} - \frac {3467}{24} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} + \frac {1309}{2} \, \sqrt {-2 \, x + 1} + \frac {5929}{16 \, \sqrt {-2 \, x + 1}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 46, normalized size = 0.70 \begin {gather*} \frac {5929}{16\,\sqrt {1-2\,x}}+\frac {1309\,\sqrt {1-2\,x}}{2}-\frac {3467\,{\left (1-2\,x\right )}^{3/2}}{24}+\frac {51\,{\left (1-2\,x\right )}^{5/2}}{2}-\frac {225\,{\left (1-2\,x\right )}^{7/2}}{112} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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