Optimal. Leaf size=27 \[ 2 x+\frac {1}{2} \left (-1-x+\frac {8}{x^2 (3+x) \log (x)}\right ) \]
[Out]
________________________________________________________________________________________
Rubi [F]
time = 0.25, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {-24-8 x+(-48-24 x) \log (x)+\left (27 x^3+18 x^4+3 x^5\right ) \log ^2(x)}{\left (18 x^3+12 x^4+2 x^5\right ) \log ^2(x)} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-24-8 x+(-48-24 x) \log (x)+\left (27 x^3+18 x^4+3 x^5\right ) \log ^2(x)}{x^3 \left (18+12 x+2 x^2\right ) \log ^2(x)} \, dx\\ &=\int \frac {-24-8 x+(-48-24 x) \log (x)+\left (27 x^3+18 x^4+3 x^5\right ) \log ^2(x)}{2 x^3 (3+x)^2 \log ^2(x)} \, dx\\ &=\frac {1}{2} \int \frac {-24-8 x+(-48-24 x) \log (x)+\left (27 x^3+18 x^4+3 x^5\right ) \log ^2(x)}{x^3 (3+x)^2 \log ^2(x)} \, dx\\ &=\frac {1}{2} \int \left (3-\frac {8}{x^3 (3+x) \log ^2(x)}-\frac {24 (2+x)}{x^3 (3+x)^2 \log (x)}\right ) \, dx\\ &=\frac {3 x}{2}-4 \int \frac {1}{x^3 (3+x) \log ^2(x)} \, dx-12 \int \frac {2+x}{x^3 (3+x)^2 \log (x)} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 1.32, size = 20, normalized size = 0.74 \begin {gather*} \frac {3 x}{2}+\frac {4}{x^2 (3+x) \log (x)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 18.74, size = 19, normalized size = 0.70
method | result | size |
risch | \(\frac {3 x}{2}+\frac {4}{x^{2} \ln \left (x \right ) \left (3+x \right )}\) | \(19\) |
norman | \(\frac {4-\frac {27 x^{2} \ln \left (x \right )}{2}+\frac {3 x^{4} \ln \left (x \right )}{2}}{x^{2} \left (3+x \right ) \ln \left (x \right )}\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.32, size = 32, normalized size = 1.19 \begin {gather*} \frac {3 \, {\left (x^{4} + 3 \, x^{3}\right )} \log \left (x\right ) + 8}{2 \, {\left (x^{3} + 3 \, x^{2}\right )} \log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.35, size = 32, normalized size = 1.19 \begin {gather*} \frac {3 \, {\left (x^{4} + 3 \, x^{3}\right )} \log \left (x\right ) + 8}{2 \, {\left (x^{3} + 3 \, x^{2}\right )} \log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.04, size = 17, normalized size = 0.63 \begin {gather*} \frac {3 x}{2} + \frac {4}{\left (x^{3} + 3 x^{2}\right ) \log {\left (x \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.41, size = 22, normalized size = 0.81 \begin {gather*} \frac {3}{2} \, x + \frac {4}{x^{3} \log \left (x\right ) + 3 \, x^{2} \log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 3.65, size = 18, normalized size = 0.67 \begin {gather*} \frac {3\,x}{2}+\frac {4}{x^2\,\ln \left (x\right )\,\left (x+3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________