Optimal. Leaf size=105 \[ -\frac{3}{128} (2 x+3)^{9/2}+\frac{81}{128} (2 x+3)^{7/2}-\frac{3519}{640} (2 x+3)^{5/2}+\frac{10475}{384} (2 x+3)^{3/2}-\frac{17201}{128} \sqrt{2 x+3}-\frac{16005}{128 \sqrt{2 x+3}}+\frac{7925}{384 (2 x+3)^{3/2}}-\frac{325}{128 (2 x+3)^{5/2}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0282774, antiderivative size = 105, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 27, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.037, Rules used = {771} \[ -\frac{3}{128} (2 x+3)^{9/2}+\frac{81}{128} (2 x+3)^{7/2}-\frac{3519}{640} (2 x+3)^{5/2}+\frac{10475}{384} (2 x+3)^{3/2}-\frac{17201}{128} \sqrt{2 x+3}-\frac{16005}{128 \sqrt{2 x+3}}+\frac{7925}{384 (2 x+3)^{3/2}}-\frac{325}{128 (2 x+3)^{5/2}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 771
Rubi steps
\begin{align*} \int \frac{(5-x) \left (2+5 x+3 x^2\right )^3}{(3+2 x)^{7/2}} \, dx &=\int \left (\frac{1625}{128 (3+2 x)^{7/2}}-\frac{7925}{128 (3+2 x)^{5/2}}+\frac{16005}{128 (3+2 x)^{3/2}}-\frac{17201}{128 \sqrt{3+2 x}}+\frac{10475}{128} \sqrt{3+2 x}-\frac{3519}{128} (3+2 x)^{3/2}+\frac{567}{128} (3+2 x)^{5/2}-\frac{27}{128} (3+2 x)^{7/2}\right ) \, dx\\ &=-\frac{325}{128 (3+2 x)^{5/2}}+\frac{7925}{384 (3+2 x)^{3/2}}-\frac{16005}{128 \sqrt{3+2 x}}-\frac{17201}{128} \sqrt{3+2 x}+\frac{10475}{384} (3+2 x)^{3/2}-\frac{3519}{640} (3+2 x)^{5/2}+\frac{81}{128} (3+2 x)^{7/2}-\frac{3}{128} (3+2 x)^{9/2}\\ \end{align*}
Mathematica [A] time = 0.0212726, size = 48, normalized size = 0.46 \[ -\frac{45 x^7-135 x^6-702 x^5-1940 x^4+3195 x^3+41805 x^2+85070 x+51162}{15 (2 x+3)^{5/2}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.004, size = 45, normalized size = 0.4 \begin{align*} -{\frac{45\,{x}^{7}-135\,{x}^{6}-702\,{x}^{5}-1940\,{x}^{4}+3195\,{x}^{3}+41805\,{x}^{2}+85070\,x+51162}{15} \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 = 1.02203, size = 93, normalized size = 0.89 \begin{align*} -\frac{3}{128} \,{\left (2 \, x + 3\right )}^{\frac{9}{2}} + \frac{81}{128} \,{\left (2 \, x + 3\right )}^{\frac{7}{2}} - \frac{3519}{640} \,{\left (2 \, x + 3\right )}^{\frac{5}{2}} + \frac{10475}{384} \,{\left (2 \, x + 3\right )}^{\frac{3}{2}} - \frac{17201}{128} \, \sqrt{2 \, x + 3} - \frac{5 \,{\left (9603 \,{\left (2 \, x + 3\right )}^{2} - 3170 \, x - 4560\right )}}{384 \,{\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 = 1.90673, size = 177, normalized size = 1.69 \begin{align*} -\frac{{\left (45 \, x^{7} - 135 \, x^{6} - 702 \, x^{5} - 1940 \, x^{4} + 3195 \, x^{3} + 41805 \, x^{2} + 85070 \, x + 51162\right )} \sqrt{2 \, x + 3}}{15 \,{\left (8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 48.7825, size = 94, normalized size = 0.9 \begin{align*} - \frac{3 \left (2 x + 3\right )^{\frac{9}{2}}}{128} + \frac{81 \left (2 x + 3\right )^{\frac{7}{2}}}{128} - \frac{3519 \left (2 x + 3\right )^{\frac{5}{2}}}{640} + \frac{10475 \left (2 x + 3\right )^{\frac{3}{2}}}{384} - \frac{17201 \sqrt{2 x + 3}}{128} - \frac{16005}{128 \sqrt{2 x + 3}} + \frac{7925}{384 \left (2 x + 3\right )^{\frac{3}{2}}} - \frac{325}{128 \left (2 x + 3\right )^{\frac{5}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.09548, size = 93, normalized size = 0.89 \begin{align*} -\frac{3}{128} \,{\left (2 \, x + 3\right )}^{\frac{9}{2}} + \frac{81}{128} \,{\left (2 \, x + 3\right )}^{\frac{7}{2}} - \frac{3519}{640} \,{\left (2 \, x + 3\right )}^{\frac{5}{2}} + \frac{10475}{384} \,{\left (2 \, x + 3\right )}^{\frac{3}{2}} - \frac{17201}{128} \, \sqrt{2 \, x + 3} - \frac{5 \,{\left (9603 \,{\left (2 \, x + 3\right )}^{2} - 3170 \, x - 4560\right )}}{384 \,{\left (2 \, x + 3\right )}^{\frac{5}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]