Optimal. Leaf size=26 \[ x \left (4+\frac {x}{e^{25} \left (x+\log \left (-2+x+\frac {9+4 x}{x^2}\right )\right )}\right ) \]
________________________________________________________________________________________
Rubi [F] time = 1.70, 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 {18 x+13 x^2+4 x^3-3 x^4+x^5+e^{25} \left (36 x^2+16 x^3-8 x^4+4 x^5\right )+\left (18 x+8 x^2-4 x^3+2 x^4+e^{25} \left (72 x+32 x^2-16 x^3+8 x^4\right )\right ) \log \left (\frac {9+4 x-2 x^2+x^3}{x^2}\right )+e^{25} \left (36+16 x-8 x^2+4 x^3\right ) \log ^2\left (\frac {9+4 x-2 x^2+x^3}{x^2}\right )}{e^{25} \left (9 x^2+4 x^3-2 x^4+x^5\right )+e^{25} \left (18 x+8 x^2-4 x^3+2 x^4\right ) \log \left (\frac {9+4 x-2 x^2+x^3}{x^2}\right )+e^{25} \left (9+4 x-2 x^2+x^3\right ) \log ^2\left (\frac {9+4 x-2 x^2+x^3}{x^2}\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {18 x+13 x^2+4 x^3-3 x^4+x^5+4 e^{25} x^2 \left (9+4 x-2 x^2+x^3\right )+2 \left (1+4 e^{25}\right ) x \left (9+4 x-2 x^2+x^3\right ) \log \left (-2+\frac {9}{x^2}+\frac {4}{x}+x\right )+4 e^{25} \left (9+4 x-2 x^2+x^3\right ) \log ^2\left (-2+\frac {9}{x^2}+\frac {4}{x}+x\right )}{e^{25} \left (9+4 x-2 x^2+x^3\right ) \left (x+\log \left (-2+\frac {9}{x^2}+\frac {4}{x}+x\right )\right )^2} \, dx\\ &=\frac {\int \frac {18 x+13 x^2+4 x^3-3 x^4+x^5+4 e^{25} x^2 \left (9+4 x-2 x^2+x^3\right )+2 \left (1+4 e^{25}\right ) x \left (9+4 x-2 x^2+x^3\right ) \log \left (-2+\frac {9}{x^2}+\frac {4}{x}+x\right )+4 e^{25} \left (9+4 x-2 x^2+x^3\right ) \log ^2\left (-2+\frac {9}{x^2}+\frac {4}{x}+x\right )}{\left (9+4 x-2 x^2+x^3\right ) \left (x+\log \left (-2+\frac {9}{x^2}+\frac {4}{x}+x\right )\right )^2} \, dx}{e^{25}}\\ &=\frac {\int \left (4 e^{25}-\frac {x \left (-18+5 x+4 x^2-x^3+x^4\right )}{\left (9+4 x-2 x^2+x^3\right ) \left (x+\log \left (-2+\frac {9}{x^2}+\frac {4}{x}+x\right )\right )^2}+\frac {2 x}{x+\log \left (-2+\frac {9}{x^2}+\frac {4}{x}+x\right )}\right ) \, dx}{e^{25}}\\ &=4 x-\frac {\int \frac {x \left (-18+5 x+4 x^2-x^3+x^4\right )}{\left (9+4 x-2 x^2+x^3\right ) \left (x+\log \left (-2+\frac {9}{x^2}+\frac {4}{x}+x\right )\right )^2} \, dx}{e^{25}}+\frac {2 \int \frac {x}{x+\log \left (-2+\frac {9}{x^2}+\frac {4}{x}+x\right )} \, dx}{e^{25}}\\ &=4 x-\frac {\int \left (\frac {2}{\left (x+\log \left (-2+\frac {9}{x^2}+\frac {4}{x}+x\right )\right )^2}+\frac {x}{\left (x+\log \left (-2+\frac {9}{x^2}+\frac {4}{x}+x\right )\right )^2}+\frac {x^2}{\left (x+\log \left (-2+\frac {9}{x^2}+\frac {4}{x}+x\right )\right )^2}+\frac {-18-35 x-4 x^2}{\left (9+4 x-2 x^2+x^3\right ) \left (x+\log \left (-2+\frac {9}{x^2}+\frac {4}{x}+x\right )\right )^2}\right ) \, dx}{e^{25}}+\frac {2 \int \frac {x}{x+\log \left (-2+\frac {9}{x^2}+\frac {4}{x}+x\right )} \, dx}{e^{25}}\\ &=4 x-\frac {\int \frac {x}{\left (x+\log \left (-2+\frac {9}{x^2}+\frac {4}{x}+x\right )\right )^2} \, dx}{e^{25}}-\frac {\int \frac {x^2}{\left (x+\log \left (-2+\frac {9}{x^2}+\frac {4}{x}+x\right )\right )^2} \, dx}{e^{25}}-\frac {\int \frac {-18-35 x-4 x^2}{\left (9+4 x-2 x^2+x^3\right ) \left (x+\log \left (-2+\frac {9}{x^2}+\frac {4}{x}+x\right )\right )^2} \, dx}{e^{25}}-\frac {2 \int \frac {1}{\left (x+\log \left (-2+\frac {9}{x^2}+\frac {4}{x}+x\right )\right )^2} \, dx}{e^{25}}+\frac {2 \int \frac {x}{x+\log \left (-2+\frac {9}{x^2}+\frac {4}{x}+x\right )} \, dx}{e^{25}}\\ &=4 x-\frac {\int \frac {x}{\left (x+\log \left (-2+\frac {9}{x^2}+\frac {4}{x}+x\right )\right )^2} \, dx}{e^{25}}-\frac {\int \frac {x^2}{\left (x+\log \left (-2+\frac {9}{x^2}+\frac {4}{x}+x\right )\right )^2} \, dx}{e^{25}}-\frac {\int \left (-\frac {18}{\left (9+4 x-2 x^2+x^3\right ) \left (x+\log \left (-2+\frac {9}{x^2}+\frac {4}{x}+x\right )\right )^2}-\frac {35 x}{\left (9+4 x-2 x^2+x^3\right ) \left (x+\log \left (-2+\frac {9}{x^2}+\frac {4}{x}+x\right )\right )^2}-\frac {4 x^2}{\left (9+4 x-2 x^2+x^3\right ) \left (x+\log \left (-2+\frac {9}{x^2}+\frac {4}{x}+x\right )\right )^2}\right ) \, dx}{e^{25}}-\frac {2 \int \frac {1}{\left (x+\log \left (-2+\frac {9}{x^2}+\frac {4}{x}+x\right )\right )^2} \, dx}{e^{25}}+\frac {2 \int \frac {x}{x+\log \left (-2+\frac {9}{x^2}+\frac {4}{x}+x\right )} \, dx}{e^{25}}\\ &=4 x-\frac {\int \frac {x}{\left (x+\log \left (-2+\frac {9}{x^2}+\frac {4}{x}+x\right )\right )^2} \, dx}{e^{25}}-\frac {\int \frac {x^2}{\left (x+\log \left (-2+\frac {9}{x^2}+\frac {4}{x}+x\right )\right )^2} \, dx}{e^{25}}-\frac {2 \int \frac {1}{\left (x+\log \left (-2+\frac {9}{x^2}+\frac {4}{x}+x\right )\right )^2} \, dx}{e^{25}}+\frac {2 \int \frac {x}{x+\log \left (-2+\frac {9}{x^2}+\frac {4}{x}+x\right )} \, dx}{e^{25}}+\frac {4 \int \frac {x^2}{\left (9+4 x-2 x^2+x^3\right ) \left (x+\log \left (-2+\frac {9}{x^2}+\frac {4}{x}+x\right )\right )^2} \, dx}{e^{25}}+\frac {18 \int \frac {1}{\left (9+4 x-2 x^2+x^3\right ) \left (x+\log \left (-2+\frac {9}{x^2}+\frac {4}{x}+x\right )\right )^2} \, dx}{e^{25}}+\frac {35 \int \frac {x}{\left (9+4 x-2 x^2+x^3\right ) \left (x+\log \left (-2+\frac {9}{x^2}+\frac {4}{x}+x\right )\right )^2} \, dx}{e^{25}}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.08, size = 33, normalized size = 1.27 \begin {gather*} \frac {4 e^{25} x+\frac {x^2}{x+\log \left (-2+\frac {9}{x^2}+\frac {4}{x}+x\right )}}{e^{25}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [B] time = 0.65, size = 63, normalized size = 2.42 \begin {gather*} \frac {4 \, x^{2} e^{25} + 4 \, x e^{25} \log \left (\frac {x^{3} - 2 \, x^{2} + 4 \, x + 9}{x^{2}}\right ) + x^{2}}{x e^{25} + e^{25} \log \left (\frac {x^{3} - 2 \, x^{2} + 4 \, x + 9}{x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.25, size = 33, normalized size = 1.27
method | result | size |
risch | \(4 x +\frac {x^{2} {\mathrm e}^{-25}}{\ln \left (\frac {x^{3}-2 x^{2}+4 x +9}{x^{2}}\right )+x}\) | \(33\) |
norman | \(\frac {\left (4 \,{\mathrm e}^{25}+1\right ) {\mathrm e}^{-25} x^{2}+4 \ln \left (\frac {x^{3}-2 x^{2}+4 x +9}{x^{2}}\right ) x}{\ln \left (\frac {x^{3}-2 x^{2}+4 x +9}{x^{2}}\right )+x}\) | \(60\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 0.42, size = 68, normalized size = 2.62 \begin {gather*} \frac {x^{2} {\left (4 \, e^{25} + 1\right )} + 4 \, x e^{25} \log \left (x^{3} - 2 \, x^{2} + 4 \, x + 9\right ) - 8 \, x e^{25} \log \relax (x)}{x e^{25} + e^{25} \log \left (x^{3} - 2 \, x^{2} + 4 \, x + 9\right ) - 2 \, e^{25} \log \relax (x)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 5.82, size = 82, normalized size = 3.15 \begin {gather*} \frac {{\mathrm {e}}^{-25}\,\left (2\,x+2\,\ln \left (\frac {x^3-2\,x^2+4\,x+9}{x^2}\right )+4\,x^2\,{\mathrm {e}}^{25}+x^2+4\,x\,{\mathrm {e}}^{25}\,\ln \left (\frac {x^3-2\,x^2+4\,x+9}{x^2}\right )\right )}{x+\ln \left (\frac {x^3-2\,x^2+4\,x+9}{x^2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.28, size = 32, normalized size = 1.23 \begin {gather*} \frac {x^{2}}{x e^{25} + e^{25} \log {\left (\frac {x^{3} - 2 x^{2} + 4 x + 9}{x^{2}} \right )}} + 4 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________