Optimal. Leaf size=66 \[ -\frac {5929}{16} \sqrt {1-2 x}+\frac {1309}{6} (1-2 x)^{3/2}-\frac {3467}{40} (1-2 x)^{5/2}+\frac {255}{14} (1-2 x)^{7/2}-\frac {25}{16} (1-2 x)^{9/2} \]
[Out]
________________________________________________________________________________________
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 {25}{16} (1-2 x)^{9/2}+\frac {255}{14} (1-2 x)^{7/2}-\frac {3467}{40} (1-2 x)^{5/2}+\frac {1309}{6} (1-2 x)^{3/2}-\frac {5929}{16} \sqrt {1-2 x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 90
Rubi steps
\begin {align*} \int \frac {(2+3 x)^2 (3+5 x)^2}{\sqrt {1-2 x}} \, dx &=\int \left (\frac {5929}{16 \sqrt {1-2 x}}-\frac {1309}{2} \sqrt {1-2 x}+\frac {3467}{8} (1-2 x)^{3/2}-\frac {255}{2} (1-2 x)^{5/2}+\frac {225}{16} (1-2 x)^{7/2}\right ) \, dx\\ &=-\frac {5929}{16} \sqrt {1-2 x}+\frac {1309}{6} (1-2 x)^{3/2}-\frac {3467}{40} (1-2 x)^{5/2}+\frac {255}{14} (1-2 x)^{7/2}-\frac {25}{16} (1-2 x)^{9/2}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.02, size = 33, normalized size = 0.50 \begin {gather*} -\frac {1}{105} \sqrt {1-2 x} \left (23354+19574 x+17391 x^2+10050 x^3+2625 x^4\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.10, size = 47, normalized size = 0.71
method | result | size |
trager | \(\left (-25 x^{4}-\frac {670}{7} x^{3}-\frac {5797}{35} x^{2}-\frac {19574}{105} x -\frac {23354}{105}\right ) \sqrt {1-2 x}\) | \(29\) |
gosper | \(-\frac {\left (2625 x^{4}+10050 x^{3}+17391 x^{2}+19574 x +23354\right ) \sqrt {1-2 x}}{105}\) | \(30\) |
risch | \(\frac {\left (-1+2 x \right ) \left (2625 x^{4}+10050 x^{3}+17391 x^{2}+19574 x +23354\right )}{105 \sqrt {1-2 x}}\) | \(35\) |
derivativedivides | \(\frac {1309 \left (1-2 x \right )^{\frac {3}{2}}}{6}-\frac {3467 \left (1-2 x \right )^{\frac {5}{2}}}{40}+\frac {255 \left (1-2 x \right )^{\frac {7}{2}}}{14}-\frac {25 \left (1-2 x \right )^{\frac {9}{2}}}{16}-\frac {5929 \sqrt {1-2 x}}{16}\) | \(47\) |
default | \(\frac {1309 \left (1-2 x \right )^{\frac {3}{2}}}{6}-\frac {3467 \left (1-2 x \right )^{\frac {5}{2}}}{40}+\frac {255 \left (1-2 x \right )^{\frac {7}{2}}}{14}-\frac {25 \left (1-2 x \right )^{\frac {9}{2}}}{16}-\frac {5929 \sqrt {1-2 x}}{16}\) | \(47\) |
meijerg | \(-\frac {18 \left (-2 \sqrt {\pi }+2 \sqrt {\pi }\, \sqrt {1-2 x}\right )}{\sqrt {\pi }}+\frac {76 \sqrt {\pi }-\frac {19 \sqrt {\pi }\, \left (8 x +8\right ) \sqrt {1-2 x}}{2}}{\sqrt {\pi }}-\frac {541 \left (-\frac {16 \sqrt {\pi }}{15}+\frac {\sqrt {\pi }\, \left (24 x^{2}+16 x +16\right ) \sqrt {1-2 x}}{15}\right )}{8 \sqrt {\pi }}+\frac {\frac {228 \sqrt {\pi }}{7}-\frac {57 \sqrt {\pi }\, \left (320 x^{3}+192 x^{2}+128 x +128\right ) \sqrt {1-2 x}}{224}}{\sqrt {\pi }}-\frac {225 \left (-\frac {256 \sqrt {\pi }}{315}+\frac {\sqrt {\pi }\, \left (1120 x^{4}+640 x^{3}+384 x^{2}+256 x +256\right ) \sqrt {1-2 x}}{315}\right )}{32 \sqrt {\pi }}\) | \(167\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.28, size = 46, normalized size = 0.70 \begin {gather*} -\frac {25}{16} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} + \frac {255}{14} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} - \frac {3467}{40} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} + \frac {1309}{6} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {5929}{16} \, \sqrt {-2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.71, size = 29, normalized size = 0.44 \begin {gather*} -\frac {1}{105} \, {\left (2625 \, x^{4} + 10050 \, x^{3} + 17391 \, x^{2} + 19574 \, x + 23354\right )} \sqrt {-2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 21.40, size = 58, normalized size = 0.88 \begin {gather*} - \frac {25 \left (1 - 2 x\right )^{\frac {9}{2}}}{16} + \frac {255 \left (1 - 2 x\right )^{\frac {7}{2}}}{14} - \frac {3467 \left (1 - 2 x\right )^{\frac {5}{2}}}{40} + \frac {1309 \left (1 - 2 x\right )^{\frac {3}{2}}}{6} - \frac {5929 \sqrt {1 - 2 x}}{16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.74, size = 67, normalized size = 1.02 \begin {gather*} -\frac {25}{16} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} - \frac {255}{14} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} - \frac {3467}{40} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} + \frac {1309}{6} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {5929}{16} \, \sqrt {-2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.02, size = 46, normalized size = 0.70 \begin {gather*} \frac {1309\,{\left (1-2\,x\right )}^{3/2}}{6}-\frac {5929\,\sqrt {1-2\,x}}{16}-\frac {3467\,{\left (1-2\,x\right )}^{5/2}}{40}+\frac {255\,{\left (1-2\,x\right )}^{7/2}}{14}-\frac {25\,{\left (1-2\,x\right )}^{9/2}}{16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________