Optimal. Leaf size=53 \[ -\frac {847}{8} \sqrt {1-2 x}+\frac {1133}{24} (1-2 x)^{3/2}-\frac {101}{8} (1-2 x)^{5/2}+\frac {75}{56} (1-2 x)^{7/2} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 53, 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 = {78}
\begin {gather*} \frac {75}{56} (1-2 x)^{7/2}-\frac {101}{8} (1-2 x)^{5/2}+\frac {1133}{24} (1-2 x)^{3/2}-\frac {847}{8} \sqrt {1-2 x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 78
Rubi steps
\begin {align*} \int \frac {(2+3 x) (3+5 x)^2}{\sqrt {1-2 x}} \, dx &=\int \left (\frac {847}{8 \sqrt {1-2 x}}-\frac {1133}{8} \sqrt {1-2 x}+\frac {505}{8} (1-2 x)^{3/2}-\frac {75}{8} (1-2 x)^{5/2}\right ) \, dx\\ &=-\frac {847}{8} \sqrt {1-2 x}+\frac {1133}{24} (1-2 x)^{3/2}-\frac {101}{8} (1-2 x)^{5/2}+\frac {75}{56} (1-2 x)^{7/2}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.02, size = 28, normalized size = 0.53 \begin {gather*} -\frac {1}{21} \sqrt {1-2 x} \left (1469+1091 x+723 x^2+225 x^3\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.10, size = 38, normalized size = 0.72
method | result | size |
trager | \(\left (-\frac {75}{7} x^{3}-\frac {241}{7} x^{2}-\frac {1091}{21} x -\frac {1469}{21}\right ) \sqrt {1-2 x}\) | \(24\) |
gosper | \(-\frac {\left (225 x^{3}+723 x^{2}+1091 x +1469\right ) \sqrt {1-2 x}}{21}\) | \(25\) |
risch | \(\frac {\left (-1+2 x \right ) \left (225 x^{3}+723 x^{2}+1091 x +1469\right )}{21 \sqrt {1-2 x}}\) | \(30\) |
derivativedivides | \(\frac {1133 \left (1-2 x \right )^{\frac {3}{2}}}{24}-\frac {101 \left (1-2 x \right )^{\frac {5}{2}}}{8}+\frac {75 \left (1-2 x \right )^{\frac {7}{2}}}{56}-\frac {847 \sqrt {1-2 x}}{8}\) | \(38\) |
default | \(\frac {1133 \left (1-2 x \right )^{\frac {3}{2}}}{24}-\frac {101 \left (1-2 x \right )^{\frac {5}{2}}}{8}+\frac {75 \left (1-2 x \right )^{\frac {7}{2}}}{56}-\frac {847 \sqrt {1-2 x}}{8}\) | \(38\) |
meijerg | \(-\frac {9 \left (-2 \sqrt {\pi }+2 \sqrt {\pi }\, \sqrt {1-2 x}\right )}{\sqrt {\pi }}+\frac {29 \sqrt {\pi }-\frac {29 \sqrt {\pi }\, \left (8 x +8\right ) \sqrt {1-2 x}}{8}}{\sqrt {\pi }}-\frac {35 \left (-\frac {16 \sqrt {\pi }}{15}+\frac {\sqrt {\pi }\, \left (24 x^{2}+16 x +16\right ) \sqrt {1-2 x}}{15}\right )}{2 \sqrt {\pi }}+\frac {\frac {30 \sqrt {\pi }}{7}-\frac {15 \sqrt {\pi }\, \left (320 x^{3}+192 x^{2}+128 x +128\right ) \sqrt {1-2 x}}{448}}{\sqrt {\pi }}\) | \(124\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.30, size = 37, normalized size = 0.70 \begin {gather*} \frac {75}{56} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} - \frac {101}{8} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} + \frac {1133}{24} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {847}{8} \, \sqrt {-2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 1.00, size = 24, normalized size = 0.45 \begin {gather*} -\frac {1}{21} \, {\left (225 \, x^{3} + 723 \, x^{2} + 1091 \, x + 1469\right )} \sqrt {-2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 14.17, size = 46, normalized size = 0.87 \begin {gather*} \frac {75 \left (1 - 2 x\right )^{\frac {7}{2}}}{56} - \frac {101 \left (1 - 2 x\right )^{\frac {5}{2}}}{8} + \frac {1133 \left (1 - 2 x\right )^{\frac {3}{2}}}{24} - \frac {847 \sqrt {1 - 2 x}}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.64, size = 51, normalized size = 0.96 \begin {gather*} -\frac {75}{56} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} - \frac {101}{8} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} + \frac {1133}{24} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {847}{8} \, \sqrt {-2 \, x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.04, size = 37, normalized size = 0.70 \begin {gather*} \frac {1133\,{\left (1-2\,x\right )}^{3/2}}{24}-\frac {847\,\sqrt {1-2\,x}}{8}-\frac {101\,{\left (1-2\,x\right )}^{5/2}}{8}+\frac {75\,{\left (1-2\,x\right )}^{7/2}}{56} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________