Optimal. Leaf size=66 \[ -\frac {135}{176} (1-2 x)^{11/2}+\frac {69}{8} (1-2 x)^{9/2}-\frac {153}{4} (1-2 x)^{7/2}+\frac {3283}{40} (1-2 x)^{5/2}-\frac {3773}{48} (1-2 x)^{3/2} \]
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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 = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {77} \[ -\frac {135}{176} (1-2 x)^{11/2}+\frac {69}{8} (1-2 x)^{9/2}-\frac {153}{4} (1-2 x)^{7/2}+\frac {3283}{40} (1-2 x)^{5/2}-\frac {3773}{48} (1-2 x)^{3/2} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin {align*} \int \sqrt {1-2 x} (2+3 x)^3 (3+5 x) \, dx &=\int \left (\frac {3773}{16} \sqrt {1-2 x}-\frac {3283}{8} (1-2 x)^{3/2}+\frac {1071}{4} (1-2 x)^{5/2}-\frac {621}{8} (1-2 x)^{7/2}+\frac {135}{16} (1-2 x)^{9/2}\right ) \, dx\\ &=-\frac {3773}{48} (1-2 x)^{3/2}+\frac {3283}{40} (1-2 x)^{5/2}-\frac {153}{4} (1-2 x)^{7/2}+\frac {69}{8} (1-2 x)^{9/2}-\frac {135}{176} (1-2 x)^{11/2}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 33, normalized size = 0.50 \[ -\frac {1}{165} (1-2 x)^{3/2} \left (2025 x^4+7335 x^3+11205 x^2+9366 x+4442\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.52, size = 34, normalized size = 0.52 \[ \frac {1}{165} \, {\left (4050 \, x^{5} + 12645 \, x^{4} + 15075 \, x^{3} + 7527 \, x^{2} - 482 \, x - 4442\right )} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.29, size = 74, normalized size = 1.12 \[ \frac {135}{176} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} + \frac {69}{8} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} + \frac {153}{4} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} + \frac {3283}{40} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} - \frac {3773}{48} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 30, normalized size = 0.45 \[ -\frac {\left (2025 x^{4}+7335 x^{3}+11205 x^{2}+9366 x +4442\right ) \left (-2 x +1\right )^{\frac {3}{2}}}{165} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.52, size = 46, normalized size = 0.70 \[ -\frac {135}{176} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} + \frac {69}{8} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - \frac {153}{4} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} + \frac {3283}{40} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} - \frac {3773}{48} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} \]
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 \[ \frac {3283\,{\left (1-2\,x\right )}^{5/2}}{40}-\frac {3773\,{\left (1-2\,x\right )}^{3/2}}{48}-\frac {153\,{\left (1-2\,x\right )}^{7/2}}{4}+\frac {69\,{\left (1-2\,x\right )}^{9/2}}{8}-\frac {135\,{\left (1-2\,x\right )}^{11/2}}{176} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 2.73, size = 58, normalized size = 0.88 \[ - \frac {135 \left (1 - 2 x\right )^{\frac {11}{2}}}{176} + \frac {69 \left (1 - 2 x\right )^{\frac {9}{2}}}{8} - \frac {153 \left (1 - 2 x\right )^{\frac {7}{2}}}{4} + \frac {3283 \left (1 - 2 x\right )^{\frac {5}{2}}}{40} - \frac {3773 \left (1 - 2 x\right )^{\frac {3}{2}}}{48} \]
Verification of antiderivative is not currently implemented for this CAS.
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