Optimal. Leaf size=92 \[ -\frac {290521}{64} \sqrt {1-2 x}+\frac {381073}{96} (1-2 x)^{3/2}-\frac {832951}{320} (1-2 x)^{5/2}+\frac {17337}{16} (1-2 x)^{7/2}-\frac {17679}{64} (1-2 x)^{9/2}+\frac {13905}{352} (1-2 x)^{11/2}-\frac {2025}{832} (1-2 x)^{13/2} \]
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Rubi [A]
time = 0.01, antiderivative size = 92, 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 {2025}{832} (1-2 x)^{13/2}+\frac {13905}{352} (1-2 x)^{11/2}-\frac {17679}{64} (1-2 x)^{9/2}+\frac {17337}{16} (1-2 x)^{7/2}-\frac {832951}{320} (1-2 x)^{5/2}+\frac {381073}{96} (1-2 x)^{3/2}-\frac {290521}{64} \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)^4 (3+5 x)^2}{\sqrt {1-2 x}} \, dx &=\int \left (\frac {290521}{64 \sqrt {1-2 x}}-\frac {381073}{32} \sqrt {1-2 x}+\frac {832951}{64} (1-2 x)^{3/2}-\frac {121359}{16} (1-2 x)^{5/2}+\frac {159111}{64} (1-2 x)^{7/2}-\frac {13905}{32} (1-2 x)^{9/2}+\frac {2025}{64} (1-2 x)^{11/2}\right ) \, dx\\ &=-\frac {290521}{64} \sqrt {1-2 x}+\frac {381073}{96} (1-2 x)^{3/2}-\frac {832951}{320} (1-2 x)^{5/2}+\frac {17337}{16} (1-2 x)^{7/2}-\frac {17679}{64} (1-2 x)^{9/2}+\frac {13905}{352} (1-2 x)^{11/2}-\frac {2025}{832} (1-2 x)^{13/2}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 43, normalized size = 0.47 \begin {gather*} -\frac {\sqrt {1-2 x} \left (4994536+4685656 x+5587044 x^2+5576580 x^3+3954645 x^4+1709100 x^5+334125 x^6\right )}{2145} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 65, normalized size = 0.71
method | result | size |
trager | \(\left (-\frac {2025}{13} x^{6}-\frac {113940}{143} x^{5}-\frac {263643}{143} x^{4}-\frac {371772}{143} x^{3}-\frac {1862348}{715} x^{2}-\frac {4685656}{2145} x -\frac {4994536}{2145}\right ) \sqrt {1-2 x}\) | \(39\) |
gosper | \(-\frac {\left (334125 x^{6}+1709100 x^{5}+3954645 x^{4}+5576580 x^{3}+5587044 x^{2}+4685656 x +4994536\right ) \sqrt {1-2 x}}{2145}\) | \(40\) |
risch | \(\frac {\left (-1+2 x \right ) \left (334125 x^{6}+1709100 x^{5}+3954645 x^{4}+5576580 x^{3}+5587044 x^{2}+4685656 x +4994536\right )}{2145 \sqrt {1-2 x}}\) | \(45\) |
derivativedivides | \(\frac {381073 \left (1-2 x \right )^{\frac {3}{2}}}{96}-\frac {832951 \left (1-2 x \right )^{\frac {5}{2}}}{320}+\frac {17337 \left (1-2 x \right )^{\frac {7}{2}}}{16}-\frac {17679 \left (1-2 x \right )^{\frac {9}{2}}}{64}+\frac {13905 \left (1-2 x \right )^{\frac {11}{2}}}{352}-\frac {2025 \left (1-2 x \right )^{\frac {13}{2}}}{832}-\frac {290521 \sqrt {1-2 x}}{64}\) | \(65\) |
default | \(\frac {381073 \left (1-2 x \right )^{\frac {3}{2}}}{96}-\frac {832951 \left (1-2 x \right )^{\frac {5}{2}}}{320}+\frac {17337 \left (1-2 x \right )^{\frac {7}{2}}}{16}-\frac {17679 \left (1-2 x \right )^{\frac {9}{2}}}{64}+\frac {13905 \left (1-2 x \right )^{\frac {11}{2}}}{352}-\frac {2025 \left (1-2 x \right )^{\frac {13}{2}}}{832}-\frac {290521 \sqrt {1-2 x}}{64}\) | \(65\) |
meijerg | \(-\frac {72 \left (-2 \sqrt {\pi }+2 \sqrt {\pi }\, \sqrt {1-2 x}\right )}{\sqrt {\pi }}+\frac {448 \sqrt {\pi }-56 \sqrt {\pi }\, \left (8 x +8\right ) \sqrt {1-2 x}}{\sqrt {\pi }}-\frac {653 \left (-\frac {16 \sqrt {\pi }}{15}+\frac {\sqrt {\pi }\, \left (24 x^{2}+16 x +16\right ) \sqrt {1-2 x}}{15}\right )}{\sqrt {\pi }}+\frac {\frac {21648 \sqrt {\pi }}{35}-\frac {1353 \sqrt {\pi }\, \left (320 x^{3}+192 x^{2}+128 x +128\right ) \sqrt {1-2 x}}{280}}{\sqrt {\pi }}-\frac {12609 \left (-\frac {256 \sqrt {\pi }}{315}+\frac {\sqrt {\pi }\, \left (1120 x^{4}+640 x^{3}+384 x^{2}+256 x +256\right ) \sqrt {1-2 x}}{315}\right )}{32 \sqrt {\pi }}+\frac {\frac {6960 \sqrt {\pi }}{77}-\frac {435 \sqrt {\pi }\, \left (8064 x^{5}+4480 x^{4}+2560 x^{3}+1536 x^{2}+1024 x +1024\right ) \sqrt {1-2 x}}{4928}}{\sqrt {\pi }}-\frac {2025 \left (-\frac {2048 \sqrt {\pi }}{3003}+\frac {\sqrt {\pi }\, \left (29568 x^{6}+16128 x^{5}+8960 x^{4}+5120 x^{3}+3072 x^{2}+2048 x +2048\right ) \sqrt {1-2 x}}{3003}\right )}{128 \sqrt {\pi }}\) | \(268\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 64, normalized size = 0.70 \begin {gather*} -\frac {2025}{832} \, {\left (-2 \, x + 1\right )}^{\frac {13}{2}} + \frac {13905}{352} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} - \frac {17679}{64} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} + \frac {17337}{16} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} - \frac {832951}{320} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} + \frac {381073}{96} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {290521}{64} \, \sqrt {-2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.75, size = 39, normalized size = 0.42 \begin {gather*} -\frac {1}{2145} \, {\left (334125 \, x^{6} + 1709100 \, x^{5} + 3954645 \, x^{4} + 5576580 \, x^{3} + 5587044 \, x^{2} + 4685656 \, x + 4994536\right )} \sqrt {-2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 38.58, size = 82, normalized size = 0.89 \begin {gather*} - \frac {2025 \left (1 - 2 x\right )^{\frac {13}{2}}}{832} + \frac {13905 \left (1 - 2 x\right )^{\frac {11}{2}}}{352} - \frac {17679 \left (1 - 2 x\right )^{\frac {9}{2}}}{64} + \frac {17337 \left (1 - 2 x\right )^{\frac {7}{2}}}{16} - \frac {832951 \left (1 - 2 x\right )^{\frac {5}{2}}}{320} + \frac {381073 \left (1 - 2 x\right )^{\frac {3}{2}}}{96} - \frac {290521 \sqrt {1 - 2 x}}{64} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.11, size = 99, normalized size = 1.08 \begin {gather*} -\frac {2025}{832} \, {\left (2 \, x - 1\right )}^{6} \sqrt {-2 \, x + 1} - \frac {13905}{352} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} - \frac {17679}{64} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} - \frac {17337}{16} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} - \frac {832951}{320} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} + \frac {381073}{96} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {290521}{64} \, \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 = 64, normalized size = 0.70 \begin {gather*} \frac {381073\,{\left (1-2\,x\right )}^{3/2}}{96}-\frac {290521\,\sqrt {1-2\,x}}{64}-\frac {832951\,{\left (1-2\,x\right )}^{5/2}}{320}+\frac {17337\,{\left (1-2\,x\right )}^{7/2}}{16}-\frac {17679\,{\left (1-2\,x\right )}^{9/2}}{64}+\frac {13905\,{\left (1-2\,x\right )}^{11/2}}{352}-\frac {2025\,{\left (1-2\,x\right )}^{13/2}}{832} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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