Optimal. Leaf size=105 \[ -\frac {3195731}{128} \sqrt {1-2 x}+\frac {3278737}{128} (1-2 x)^{3/2}-\frac {12973191}{640} (1-2 x)^{5/2}+\frac {1357793}{128} (1-2 x)^{7/2}-\frac {1392467}{384} (1-2 x)^{9/2}+\frac {1101465 (1-2 x)^{11/2}}{1408}-\frac {161325 (1-2 x)^{13/2}}{1664}+\frac {675}{128} (1-2 x)^{15/2} \]
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Rubi [A]
time = 0.01, antiderivative size = 105, 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 {675}{128} (1-2 x)^{15/2}-\frac {161325 (1-2 x)^{13/2}}{1664}+\frac {1101465 (1-2 x)^{11/2}}{1408}-\frac {1392467}{384} (1-2 x)^{9/2}+\frac {1357793}{128} (1-2 x)^{7/2}-\frac {12973191}{640} (1-2 x)^{5/2}+\frac {3278737}{128} (1-2 x)^{3/2}-\frac {3195731}{128} \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)^3}{\sqrt {1-2 x}} \, dx &=\int \left (\frac {3195731}{128 \sqrt {1-2 x}}-\frac {9836211}{128} \sqrt {1-2 x}+\frac {12973191}{128} (1-2 x)^{3/2}-\frac {9504551}{128} (1-2 x)^{5/2}+\frac {4177401}{128} (1-2 x)^{7/2}-\frac {1101465}{128} (1-2 x)^{9/2}+\frac {161325}{128} (1-2 x)^{11/2}-\frac {10125}{128} (1-2 x)^{13/2}\right ) \, dx\\ &=-\frac {3195731}{128} \sqrt {1-2 x}+\frac {3278737}{128} (1-2 x)^{3/2}-\frac {12973191}{640} (1-2 x)^{5/2}+\frac {1357793}{128} (1-2 x)^{7/2}-\frac {1392467}{384} (1-2 x)^{9/2}+\frac {1101465 (1-2 x)^{11/2}}{1408}-\frac {161325 (1-2 x)^{13/2}}{1664}+\frac {675}{128} (1-2 x)^{15/2}\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 48, normalized size = 0.46 \begin {gather*} -\frac {\sqrt {1-2 x} \left (25632688+24706048 x+31962552 x^2+37260640 x^3+33786160 x^4+21369825 x^5+8241750 x^6+1447875 x^7\right )}{2145} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 74, normalized size = 0.70
method | result | size |
trager | \(\left (-675 x^{7}-\frac {49950}{13} x^{6}-\frac {1424655}{143} x^{5}-\frac {6757232}{429} x^{4}-\frac {7452128}{429} x^{3}-\frac {10654184}{715} x^{2}-\frac {24706048}{2145} x -\frac {25632688}{2145}\right ) \sqrt {1-2 x}\) | \(44\) |
gosper | \(-\frac {\left (1447875 x^{7}+8241750 x^{6}+21369825 x^{5}+33786160 x^{4}+37260640 x^{3}+31962552 x^{2}+24706048 x +25632688\right ) \sqrt {1-2 x}}{2145}\) | \(45\) |
risch | \(\frac {\left (-1+2 x \right ) \left (1447875 x^{7}+8241750 x^{6}+21369825 x^{5}+33786160 x^{4}+37260640 x^{3}+31962552 x^{2}+24706048 x +25632688\right )}{2145 \sqrt {1-2 x}}\) | \(50\) |
derivativedivides | \(\frac {3278737 \left (1-2 x \right )^{\frac {3}{2}}}{128}-\frac {12973191 \left (1-2 x \right )^{\frac {5}{2}}}{640}+\frac {1357793 \left (1-2 x \right )^{\frac {7}{2}}}{128}-\frac {1392467 \left (1-2 x \right )^{\frac {9}{2}}}{384}+\frac {1101465 \left (1-2 x \right )^{\frac {11}{2}}}{1408}-\frac {161325 \left (1-2 x \right )^{\frac {13}{2}}}{1664}+\frac {675 \left (1-2 x \right )^{\frac {15}{2}}}{128}-\frac {3195731 \sqrt {1-2 x}}{128}\) | \(74\) |
default | \(\frac {3278737 \left (1-2 x \right )^{\frac {3}{2}}}{128}-\frac {12973191 \left (1-2 x \right )^{\frac {5}{2}}}{640}+\frac {1357793 \left (1-2 x \right )^{\frac {7}{2}}}{128}-\frac {1392467 \left (1-2 x \right )^{\frac {9}{2}}}{384}+\frac {1101465 \left (1-2 x \right )^{\frac {11}{2}}}{1408}-\frac {161325 \left (1-2 x \right )^{\frac {13}{2}}}{1664}+\frac {675 \left (1-2 x \right )^{\frac {15}{2}}}{128}-\frac {3195731 \sqrt {1-2 x}}{128}\) | \(74\) |
meijerg | \(-\frac {216 \left (-2 \sqrt {\pi }+2 \sqrt {\pi }\, \sqrt {1-2 x}\right )}{\sqrt {\pi }}+\frac {1584 \sqrt {\pi }-198 \sqrt {\pi }\, \left (8 x +8\right ) \sqrt {1-2 x}}{\sqrt {\pi }}-\frac {2799 \left (-\frac {16 \sqrt {\pi }}{15}+\frac {\sqrt {\pi }\, \left (24 x^{2}+16 x +16\right ) \sqrt {1-2 x}}{15}\right )}{\sqrt {\pi }}+\frac {\frac {117184 \sqrt {\pi }}{35}-\frac {1831 \sqrt {\pi }\, \left (320 x^{3}+192 x^{2}+128 x +128\right ) \sqrt {1-2 x}}{70}}{\sqrt {\pi }}-\frac {91947 \left (-\frac {256 \sqrt {\pi }}{315}+\frac {\sqrt {\pi }\, \left (1120 x^{4}+640 x^{3}+384 x^{2}+256 x +256\right ) \sqrt {1-2 x}}{315}\right )}{32 \sqrt {\pi }}+\frac {\frac {76920 \sqrt {\pi }}{77}-\frac {9615 \sqrt {\pi }\, \left (8064 x^{5}+4480 x^{4}+2560 x^{3}+1536 x^{2}+1024 x +1024\right ) \sqrt {1-2 x}}{9856}}{\sqrt {\pi }}-\frac {45225 \left (-\frac {2048 \sqrt {\pi }}{3003}+\frac {\sqrt {\pi }\, \left (29568 x^{6}+16128 x^{5}+8960 x^{4}+5120 x^{3}+3072 x^{2}+2048 x +2048\right ) \sqrt {1-2 x}}{3003}\right )}{128 \sqrt {\pi }}+\frac {\frac {3600 \sqrt {\pi }}{143}-\frac {225 \sqrt {\pi }\, \left (878592 x^{7}+473088 x^{6}+258048 x^{5}+143360 x^{4}+81920 x^{3}+49152 x^{2}+32768 x +32768\right ) \sqrt {1-2 x}}{292864}}{\sqrt {\pi }}\) | \(326\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 73, normalized size = 0.70 \begin {gather*} \frac {675}{128} \, {\left (-2 \, x + 1\right )}^{\frac {15}{2}} - \frac {161325}{1664} \, {\left (-2 \, x + 1\right )}^{\frac {13}{2}} + \frac {1101465}{1408} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} - \frac {1392467}{384} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} + \frac {1357793}{128} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} - \frac {12973191}{640} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} + \frac {3278737}{128} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {3195731}{128} \, \sqrt {-2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.20, size = 44, normalized size = 0.42 \begin {gather*} -\frac {1}{2145} \, {\left (1447875 \, x^{7} + 8241750 \, x^{6} + 21369825 \, x^{5} + 33786160 \, x^{4} + 37260640 \, x^{3} + 31962552 \, x^{2} + 24706048 \, x + 25632688\right )} \sqrt {-2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 52.35, size = 94, normalized size = 0.90 \begin {gather*} \frac {675 \left (1 - 2 x\right )^{\frac {15}{2}}}{128} - \frac {161325 \left (1 - 2 x\right )^{\frac {13}{2}}}{1664} + \frac {1101465 \left (1 - 2 x\right )^{\frac {11}{2}}}{1408} - \frac {1392467 \left (1 - 2 x\right )^{\frac {9}{2}}}{384} + \frac {1357793 \left (1 - 2 x\right )^{\frac {7}{2}}}{128} - \frac {12973191 \left (1 - 2 x\right )^{\frac {5}{2}}}{640} + \frac {3278737 \left (1 - 2 x\right )^{\frac {3}{2}}}{128} - \frac {3195731 \sqrt {1 - 2 x}}{128} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.79, size = 115, normalized size = 1.10 \begin {gather*} -\frac {675}{128} \, {\left (2 \, x - 1\right )}^{7} \sqrt {-2 \, x + 1} - \frac {161325}{1664} \, {\left (2 \, x - 1\right )}^{6} \sqrt {-2 \, x + 1} - \frac {1101465}{1408} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} - \frac {1392467}{384} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} - \frac {1357793}{128} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} - \frac {12973191}{640} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} + \frac {3278737}{128} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {3195731}{128} \, \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 = 73, normalized size = 0.70 \begin {gather*} \frac {3278737\,{\left (1-2\,x\right )}^{3/2}}{128}-\frac {3195731\,\sqrt {1-2\,x}}{128}-\frac {12973191\,{\left (1-2\,x\right )}^{5/2}}{640}+\frac {1357793\,{\left (1-2\,x\right )}^{7/2}}{128}-\frac {1392467\,{\left (1-2\,x\right )}^{9/2}}{384}+\frac {1101465\,{\left (1-2\,x\right )}^{11/2}}{1408}-\frac {161325\,{\left (1-2\,x\right )}^{13/2}}{1664}+\frac {675\,{\left (1-2\,x\right )}^{15/2}}{128} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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