Optimal. Leaf size=53 \[ -\frac{3}{88} (2 x+3)^{11/2}+\frac{47}{72} (2 x+3)^{9/2}-\frac{109}{56} (2 x+3)^{7/2}+\frac{13}{8} (2 x+3)^{5/2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0197465, antiderivative size = 53, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.04, Rules used = {771} \[ -\frac{3}{88} (2 x+3)^{11/2}+\frac{47}{72} (2 x+3)^{9/2}-\frac{109}{56} (2 x+3)^{7/2}+\frac{13}{8} (2 x+3)^{5/2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 771
Rubi steps
\begin{align*} \int (5-x) (3+2 x)^{3/2} \left (2+5 x+3 x^2\right ) \, dx &=\int \left (\frac{65}{8} (3+2 x)^{3/2}-\frac{109}{8} (3+2 x)^{5/2}+\frac{47}{8} (3+2 x)^{7/2}-\frac{3}{8} (3+2 x)^{9/2}\right ) \, dx\\ &=\frac{13}{8} (3+2 x)^{5/2}-\frac{109}{56} (3+2 x)^{7/2}+\frac{47}{72} (3+2 x)^{9/2}-\frac{3}{88} (3+2 x)^{11/2}\\ \end{align*}
Mathematica [A] time = 0.011594, size = 28, normalized size = 0.53 \[ -\frac{1}{693} (2 x+3)^{5/2} \left (189 x^3-959 x^2-1455 x-513\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.003, size = 25, normalized size = 0.5 \begin{align*} -{\frac{189\,{x}^{3}-959\,{x}^{2}-1455\,x-513}{693} \left ( 3+2\,x \right ) ^{{\frac{5}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.05848, size = 50, normalized size = 0.94 \begin{align*} -\frac{3}{88} \,{\left (2 \, x + 3\right )}^{\frac{11}{2}} + \frac{47}{72} \,{\left (2 \, x + 3\right )}^{\frac{9}{2}} - \frac{109}{56} \,{\left (2 \, x + 3\right )}^{\frac{7}{2}} + \frac{13}{8} \,{\left (2 \, x + 3\right )}^{\frac{5}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.90197, size = 113, normalized size = 2.13 \begin{align*} -\frac{1}{693} \,{\left (756 \, x^{5} - 1568 \, x^{4} - 15627 \, x^{3} - 28143 \, x^{2} - 19251 \, x - 4617\right )} \sqrt{2 \, x + 3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 11.973, size = 46, normalized size = 0.87 \begin{align*} - \frac{3 \left (2 x + 3\right )^{\frac{11}{2}}}{88} + \frac{47 \left (2 x + 3\right )^{\frac{9}{2}}}{72} - \frac{109 \left (2 x + 3\right )^{\frac{7}{2}}}{56} + \frac{13 \left (2 x + 3\right )^{\frac{5}{2}}}{8} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.09702, size = 50, normalized size = 0.94 \begin{align*} -\frac{3}{88} \,{\left (2 \, x + 3\right )}^{\frac{11}{2}} + \frac{47}{72} \,{\left (2 \, x + 3\right )}^{\frac{9}{2}} - \frac{109}{56} \,{\left (2 \, x + 3\right )}^{\frac{7}{2}} + \frac{13}{8} \,{\left (2 \, x + 3\right )}^{\frac{5}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]