Optimal. Leaf size=92 \[ -\frac {2025}{832} (1-2 x)^{13/2}+\frac {13905}{352} (1-2 x)^{11/2}-\frac {17679}{64} (1-2 x)^{9/2}+\frac {17337}{16} (1-2 x)^{7/2}-\frac {832951}{320} (1-2 x)^{5/2}+\frac {381073}{96} (1-2 x)^{3/2}-\frac {290521}{64} \sqrt {1-2 x} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.02, 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 = {88} \[ -\frac {2025}{832} (1-2 x)^{13/2}+\frac {13905}{352} (1-2 x)^{11/2}-\frac {17679}{64} (1-2 x)^{9/2}+\frac {17337}{16} (1-2 x)^{7/2}-\frac {832951}{320} (1-2 x)^{5/2}+\frac {381073}{96} (1-2 x)^{3/2}-\frac {290521}{64} \sqrt {1-2 x} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 88
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*}
________________________________________________________________________________________
Mathematica [A] time = 0.02, size = 43, normalized size = 0.47 \[ -\frac {\sqrt {1-2 x} \left (334125 x^6+1709100 x^5+3954645 x^4+5576580 x^3+5587044 x^2+4685656 x+4994536\right )}{2145} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.09, size = 39, normalized size = 0.42 \[ -\frac {1}{2145} \, {\left (334125 \, x^{6} + 1709100 \, x^{5} + 3954645 \, x^{4} + 5576580 \, x^{3} + 5587044 \, x^{2} + 4685656 \, x + 4994536\right )} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.93, size = 99, normalized size = 1.08 \[ -\frac {2025}{832} \, {\left (2 \, x - 1\right )}^{6} \sqrt {-2 \, x + 1} - \frac {13905}{352} \, {\left (2 \, x - 1\right )}^{5} \sqrt {-2 \, x + 1} - \frac {17679}{64} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} - \frac {17337}{16} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} - \frac {832951}{320} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} + \frac {381073}{96} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {290521}{64} \, \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 40, normalized size = 0.43 \[ -\frac {\left (334125 x^{6}+1709100 x^{5}+3954645 x^{4}+5576580 x^{3}+5587044 x^{2}+4685656 x +4994536\right ) \sqrt {-2 x +1}}{2145} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.43, size = 64, normalized size = 0.70 \[ -\frac {2025}{832} \, {\left (-2 \, x + 1\right )}^{\frac {13}{2}} + \frac {13905}{352} \, {\left (-2 \, x + 1\right )}^{\frac {11}{2}} - \frac {17679}{64} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} + \frac {17337}{16} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} - \frac {832951}{320} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} + \frac {381073}{96} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {290521}{64} \, \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.03, size = 64, normalized size = 0.70 \[ \frac {381073\,{\left (1-2\,x\right )}^{3/2}}{96}-\frac {290521\,\sqrt {1-2\,x}}{64}-\frac {832951\,{\left (1-2\,x\right )}^{5/2}}{320}+\frac {17337\,{\left (1-2\,x\right )}^{7/2}}{16}-\frac {17679\,{\left (1-2\,x\right )}^{9/2}}{64}+\frac {13905\,{\left (1-2\,x\right )}^{11/2}}{352}-\frac {2025\,{\left (1-2\,x\right )}^{13/2}}{832} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 89.64, size = 82, normalized size = 0.89 \[ - \frac {2025 \left (1 - 2 x\right )^{\frac {13}{2}}}{832} + \frac {13905 \left (1 - 2 x\right )^{\frac {11}{2}}}{352} - \frac {17679 \left (1 - 2 x\right )^{\frac {9}{2}}}{64} + \frac {17337 \left (1 - 2 x\right )^{\frac {7}{2}}}{16} - \frac {832951 \left (1 - 2 x\right )^{\frac {5}{2}}}{320} + \frac {381073 \left (1 - 2 x\right )^{\frac {3}{2}}}{96} - \frac {290521 \sqrt {1 - 2 x}}{64} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________