Optimal. Leaf size=66 \[ -\frac {15}{16} (1-2 x)^{9/2}+\frac {621}{56} (1-2 x)^{7/2}-\frac {1071}{20} (1-2 x)^{5/2}+\frac {3283}{24} (1-2 x)^{3/2}-\frac {3773}{16} \sqrt {1-2 x} \]
[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 = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {77} \[ -\frac {15}{16} (1-2 x)^{9/2}+\frac {621}{56} (1-2 x)^{7/2}-\frac {1071}{20} (1-2 x)^{5/2}+\frac {3283}{24} (1-2 x)^{3/2}-\frac {3773}{16} \sqrt {1-2 x} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 77
Rubi steps
\begin {align*} \int \frac {(2+3 x)^3 (3+5 x)}{\sqrt {1-2 x}} \, dx &=\int \left (\frac {3773}{16 \sqrt {1-2 x}}-\frac {3283}{8} \sqrt {1-2 x}+\frac {1071}{4} (1-2 x)^{3/2}-\frac {621}{8} (1-2 x)^{5/2}+\frac {135}{16} (1-2 x)^{7/2}\right ) \, dx\\ &=-\frac {3773}{16} \sqrt {1-2 x}+\frac {3283}{24} (1-2 x)^{3/2}-\frac {1071}{20} (1-2 x)^{5/2}+\frac {621}{56} (1-2 x)^{7/2}-\frac {15}{16} (1-2 x)^{9/2}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.02, size = 33, normalized size = 0.50 \[ -\frac {1}{105} \sqrt {1-2 x} \left (1575 x^4+6165 x^3+10881 x^2+12434 x+14954\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.08, size = 29, normalized size = 0.44 \[ -\frac {1}{105} \, {\left (1575 \, x^{4} + 6165 \, x^{3} + 10881 \, x^{2} + 12434 \, x + 14954\right )} \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.09, size = 67, normalized size = 1.02 \[ -\frac {15}{16} \, {\left (2 \, x - 1\right )}^{4} \sqrt {-2 \, x + 1} - \frac {621}{56} \, {\left (2 \, x - 1\right )}^{3} \sqrt {-2 \, x + 1} - \frac {1071}{20} \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} + \frac {3283}{24} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {3773}{16} \, \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 30, normalized size = 0.45 \[ -\frac {\left (1575 x^{4}+6165 x^{3}+10881 x^{2}+12434 x +14954\right ) \sqrt {-2 x +1}}{105} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.48, size = 46, normalized size = 0.70 \[ -\frac {15}{16} \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} + \frac {621}{56} \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} - \frac {1071}{20} \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} + \frac {3283}{24} \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - \frac {3773}{16} \, \sqrt {-2 \, x + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.02, size = 46, normalized size = 0.70 \[ \frac {3283\,{\left (1-2\,x\right )}^{3/2}}{24}-\frac {3773\,\sqrt {1-2\,x}}{16}-\frac {1071\,{\left (1-2\,x\right )}^{5/2}}{20}+\frac {621\,{\left (1-2\,x\right )}^{7/2}}{56}-\frac {15\,{\left (1-2\,x\right )}^{9/2}}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 44.15, size = 58, normalized size = 0.88 \[ - \frac {15 \left (1 - 2 x\right )^{\frac {9}{2}}}{16} + \frac {621 \left (1 - 2 x\right )^{\frac {7}{2}}}{56} - \frac {1071 \left (1 - 2 x\right )^{\frac {5}{2}}}{20} + \frac {3283 \left (1 - 2 x\right )^{\frac {3}{2}}}{24} - \frac {3773 \sqrt {1 - 2 x}}{16} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________