Optimal. Leaf size=92 \[ -\frac {1215}{832} (1-2 x)^{13/2}+\frac {1053}{44} (1-2 x)^{11/2}-\frac {10815}{64} (1-2 x)^{9/2}+\frac {5355}{8} (1-2 x)^{7/2}-\frac {103929}{64} (1-2 x)^{5/2}+\frac {60025}{24} (1-2 x)^{3/2}-\frac {184877}{64} \sqrt {1-2 x} \]
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Rubi [A] time = 0.02, antiderivative size = 92, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {77} \[ -\frac {1215}{832} (1-2 x)^{13/2}+\frac {1053}{44} (1-2 x)^{11/2}-\frac {10815}{64} (1-2 x)^{9/2}+\frac {5355}{8} (1-2 x)^{7/2}-\frac {103929}{64} (1-2 x)^{5/2}+\frac {60025}{24} (1-2 x)^{3/2}-\frac {184877}{64} \sqrt {1-2 x} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \frac {(2+3 x)^5 (3+5 x)}{\sqrt {1-2 x}} \, dx &=\int \left (\frac {184877}{64 \sqrt {1-2 x}}-\frac {60025}{8} \sqrt {1-2 x}+\frac {519645}{64} (1-2 x)^{3/2}-\frac {37485}{8} (1-2 x)^{5/2}+\frac {97335}{64} (1-2 x)^{7/2}-\frac {1053}{4} (1-2 x)^{9/2}+\frac {1215}{64} (1-2 x)^{11/2}\right ) \, dx\\ &=-\frac {184877}{64} \sqrt {1-2 x}+\frac {60025}{24} (1-2 x)^{3/2}-\frac {103929}{64} (1-2 x)^{5/2}+\frac {5355}{8} (1-2 x)^{7/2}-\frac {10815}{64} (1-2 x)^{9/2}+\frac {1053}{44} (1-2 x)^{11/2}-\frac {1215}{832} (1-2 x)^{13/2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 43, normalized size = 0.47 \[ -\frac {1}{429} \sqrt {1-2 x} \left (40095 x^6+208251 x^5+488925 x^4+698580 x^3+707436 x^2+597464 x+638648\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.93, size = 39, normalized size = 0.42 \[ -\frac {1}{429} \, {\left (40095 \, x^{6} + 208251 \, x^{5} + 488925 \, x^{4} + 698580 \, x^{3} + 707436 \, x^{2} + 597464 \, x + 638648\right )} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.03, size = 99, normalized size = 1.08 \[ -\frac {1215}{832} \, {\left (2 \, x - 1\right )}^{6} \sqrt {-2 \, x + 1} - \frac {1053}{44} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} - \frac {10815}{64} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} - \frac {5355}{8} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} - \frac {103929}{64} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} + \frac {60025}{24} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {184877}{64} \, \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 40, normalized size = 0.43 \[ -\frac {\left (40095 x^{6}+208251 x^{5}+488925 x^{4}+698580 x^{3}+707436 x^{2}+597464 x +638648\right ) \sqrt {-2 x +1}}{429} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 64, normalized size = 0.70 \[ -\frac {1215}{832} \, {\left (-2 \, x + 1\right )}^{\frac {13}{2}} + \frac {1053}{44} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} - \frac {10815}{64} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} + \frac {5355}{8} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} - \frac {103929}{64} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} + \frac {60025}{24} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {184877}{64} \, \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 64, normalized size = 0.70 \[ \frac {60025\,{\left (1-2\,x\right )}^{3/2}}{24}-\frac {184877\,\sqrt {1-2\,x}}{64}-\frac {103929\,{\left (1-2\,x\right )}^{5/2}}{64}+\frac {5355\,{\left (1-2\,x\right )}^{7/2}}{8}-\frac {10815\,{\left (1-2\,x\right )}^{9/2}}{64}+\frac {1053\,{\left (1-2\,x\right )}^{11/2}}{44}-\frac {1215\,{\left (1-2\,x\right )}^{13/2}}{832} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 89.56, size = 82, normalized size = 0.89 \[ - \frac {1215 \left (1 - 2 x\right )^{\frac {13}{2}}}{832} + \frac {1053 \left (1 - 2 x\right )^{\frac {11}{2}}}{44} - \frac {10815 \left (1 - 2 x\right )^{\frac {9}{2}}}{64} + \frac {5355 \left (1 - 2 x\right )^{\frac {7}{2}}}{8} - \frac {103929 \left (1 - 2 x\right )^{\frac {5}{2}}}{64} + \frac {60025 \left (1 - 2 x\right )^{\frac {3}{2}}}{24} - \frac {184877 \sqrt {1 - 2 x}}{64} \]
Verification of antiderivative is not currently implemented for this CAS.
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