Optimal. Leaf size=34 \[ -\frac{16}{27 x^{3/2}}-\frac{2 \log ^2(x)}{3 x^{3/2}}-\frac{8 \log (x)}{9 x^{3/2}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0202339, antiderivative size = 34, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2, Rules used = {2305, 2304} \[ -\frac{16}{27 x^{3/2}}-\frac{2 \log ^2(x)}{3 x^{3/2}}-\frac{8 \log (x)}{9 x^{3/2}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2305
Rule 2304
Rubi steps
\begin{align*} \int \frac{\log ^2(x)}{x^{5/2}} \, dx &=-\frac{2 \log ^2(x)}{3 x^{3/2}}+\frac{4}{3} \int \frac{\log (x)}{x^{5/2}} \, dx\\ &=-\frac{16}{27 x^{3/2}}-\frac{8 \log (x)}{9 x^{3/2}}-\frac{2 \log ^2(x)}{3 x^{3/2}}\\ \end{align*}
Mathematica [A] time = 0.0068995, size = 21, normalized size = 0.62 \[ -\frac{2 \left (9 \log ^2(x)+12 \log (x)+8\right )}{27 x^{3/2}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.016, size = 23, normalized size = 0.7 \begin{align*} -{\frac{16}{27}{x}^{-{\frac{3}{2}}}}-{\frac{8\,\ln \left ( x \right ) }{9}{x}^{-{\frac{3}{2}}}}-{\frac{2\, \left ( \ln \left ( x \right ) \right ) ^{2}}{3}{x}^{-{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.955466, size = 30, normalized size = 0.88 \begin{align*} -\frac{2 \, \log \left (x\right )^{2}}{3 \, x^{\frac{3}{2}}} - \frac{8 \, \log \left (x\right )}{9 \, x^{\frac{3}{2}}} - \frac{16}{27 \, x^{\frac{3}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 2.15775, size = 59, normalized size = 1.74 \begin{align*} -\frac{2 \,{\left (9 \, \log \left (x\right )^{2} + 12 \, \log \left (x\right ) + 8\right )}}{27 \, x^{\frac{3}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 6.13746, size = 34, normalized size = 1. \begin{align*} - \frac{2 \log{\left (x \right )}^{2}}{3 x^{\frac{3}{2}}} - \frac{8 \log{\left (x \right )}}{9 x^{\frac{3}{2}}} - \frac{16}{27 x^{\frac{3}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.16687, size = 30, normalized size = 0.88 \begin{align*} -\frac{2 \, \log \left (x\right )^{2}}{3 \, x^{\frac{3}{2}}} - \frac{8 \, \log \left (x\right )}{9 \, x^{\frac{3}{2}}} - \frac{16}{27 \, x^{\frac{3}{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]