Optimal. Leaf size=23 \[ \frac {2 x^{3/2}}{15}+\frac {2 x^{5/2}}{5}-2 \log (x) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.00, antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 0, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \frac {2 x^{5/2}}{5}+\frac {2 x^{3/2}}{15}-2 \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rubi steps
\begin {align*} \int \left (-\frac {2}{x}+\frac {\sqrt {x}}{5}+x^{3/2}\right ) \, dx &=\frac {2 x^{3/2}}{15}+\frac {2 x^{5/2}}{5}-2 \log (x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 23, normalized size = 1.00 \begin {gather*} \frac {2 x^{3/2}}{15}+\frac {2 x^{5/2}}{5}-2 \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.04, size = 16, normalized size = 0.70
method | result | size |
derivativedivides | \(\frac {2 x^{\frac {3}{2}}}{15}+\frac {2 x^{\frac {5}{2}}}{5}-2 \ln \left (x \right )\) | \(16\) |
default | \(\frac {2 x^{\frac {3}{2}}}{15}+\frac {2 x^{\frac {5}{2}}}{5}-2 \ln \left (x \right )\) | \(16\) |
trager | \(\frac {2 x^{\frac {3}{2}} \left (1+3 x \right )}{15}-2 \ln \left (x \right )\) | \(16\) |
risch | \(\frac {2 x^{\frac {3}{2}}}{15}+\frac {2 x^{\frac {5}{2}}}{5}-2 \ln \left (x \right )\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.29, size = 15, normalized size = 0.65 \begin {gather*} \frac {2}{5} \, x^{\frac {5}{2}} + \frac {2}{15} \, x^{\frac {3}{2}} - 2 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 1.01, size = 19, normalized size = 0.83 \begin {gather*} \frac {2}{15} \, {\left (3 \, x^{2} + x\right )} \sqrt {x} - 4 \, \log \left (\sqrt {x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.01, size = 20, normalized size = 0.87 \begin {gather*} \frac {2 x^{\frac {5}{2}}}{5} + \frac {2 x^{\frac {3}{2}}}{15} - 2 \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 1.49, size = 16, normalized size = 0.70 \begin {gather*} \frac {2}{5} \, x^{\frac {5}{2}} + \frac {2}{15} \, x^{\frac {3}{2}} - 2 \, \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.28, size = 17, normalized size = 0.74 \begin {gather*} \frac {2\,x^{3/2}}{15}-4\,\ln \left (\sqrt {x}\right )+\frac {2\,x^{5/2}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________