Optimal. Leaf size=18 \[ e^{\left (3+\frac {x}{2}+x^{-2+x}\right )^2}+x \]
[Out]
________________________________________________________________________________________
Rubi [F]
time = 2.81, 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 {2 x^5+\exp \left (\frac {36 x^4+12 x^5+x^6+4 x^{2 x}+x^x \left (24 x^2+4 x^3\right )}{4 x^4}\right ) \left (6 x^5+x^6+x^{2 x} (-8+4 x+4 x \log (x))+x^x \left (-24 x^2+10 x^3+2 x^4+\left (12 x^3+2 x^4\right ) \log (x)\right )\right )}{2 x^5} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int \frac {2 x^5+\exp \left (\frac {36 x^4+12 x^5+x^6+4 x^{2 x}+x^x \left (24 x^2+4 x^3\right )}{4 x^4}\right ) \left (6 x^5+x^6+x^{2 x} (-8+4 x+4 x \log (x))+x^x \left (-24 x^2+10 x^3+2 x^4+\left (12 x^3+2 x^4\right ) \log (x)\right )\right )}{x^5} \, dx\\ &=\frac {1}{2} \int \left (2+6 e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}}+e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x+4 e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-5+2 x} (-2+x+x \log (x))+2 e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-3+x} \left (-12+5 x+x^2+6 x \log (x)+x^2 \log (x)\right )\right ) \, dx\\ &=x+\frac {1}{2} \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x \, dx+2 \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-5+2 x} (-2+x+x \log (x)) \, dx+3 \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} \, dx+\int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-3+x} \left (-12+5 x+x^2+6 x \log (x)+x^2 \log (x)\right ) \, dx\\ &=x+\frac {1}{2} \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x \, dx+2 \int \left (-2 e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-5+2 x}+e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-4+2 x}+e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-4+2 x} \log (x)\right ) \, dx+3 \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} \, dx+\int \left (-12 e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-3+x}+5 e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-2+x}+e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-1+x}+6 e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-2+x} \log (x)+e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-1+x} \log (x)\right ) \, dx\\ &=x+\frac {1}{2} \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x \, dx+2 \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-4+2 x} \, dx+2 \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-4+2 x} \log (x) \, dx+3 \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} \, dx-4 \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-5+2 x} \, dx+5 \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-2+x} \, dx+6 \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-2+x} \log (x) \, dx-12 \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-3+x} \, dx+\int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-1+x} \, dx+\int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-1+x} \log (x) \, dx\\ &=x+\frac {1}{2} \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x \, dx+2 \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-4+2 x} \, dx-2 \int \frac {\int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-4+2 x} \, dx}{x} \, dx+3 \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} \, dx-4 \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-5+2 x} \, dx+5 \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-2+x} \, dx-6 \int \frac {\int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-2+x} \, dx}{x} \, dx-12 \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-3+x} \, dx+\log (x) \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-1+x} \, dx+(2 \log (x)) \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-4+2 x} \, dx+(6 \log (x)) \int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-2+x} \, dx+\int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-1+x} \, dx-\int \frac {\int e^{\frac {\left (6 x^2+x^3+2 x^x\right )^2}{4 x^4}} x^{-1+x} \, dx}{x} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 2.20, size = 32, normalized size = 1.78 \begin {gather*} e^{9+3 x+\frac {x^2}{4}+x^{-4+2 x}+x^{-2+x} (6+x)}+x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.38, size = 25, normalized size = 1.39
method | result | size |
risch | \(x +{\mathrm e}^{\frac {\left (x^{3}+6 x^{2}+2 x^{x}\right )^{2}}{4 x^{4}}}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 37 vs.
\(2 (18) = 36\).
time = 0.38, size = 37, normalized size = 2.06 \begin {gather*} x + e^{\left (\frac {1}{4} \, x^{2} + 3 \, x + \frac {x^{x}}{x} + \frac {6 \, x^{x}}{x^{2}} + \frac {x^{2 \, x}}{x^{4}} + 9\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 43 vs.
\(2 (18) = 36\).
time = 0.39, size = 43, normalized size = 2.39 \begin {gather*} x + e^{\left (\frac {x^{6} + 12 \, x^{5} + 36 \, x^{4} + 4 \, {\left (x^{3} + 6 \, x^{2}\right )} x^{x} + 4 \, x^{2 \, x}}{4 \, x^{4}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 48 vs.
\(2 (19) = 38\).
time = 0.56, size = 48, normalized size = 2.67 \begin {gather*} x + e^{\frac {\frac {x^{6}}{4} + 3 x^{5} + 9 x^{4} + \frac {\left (4 x^{3} + 24 x^{2}\right ) e^{x \log {\left (x \right )}}}{4} + e^{2 x \log {\left (x \right )}}}{x^{4}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 5.64, size = 42, normalized size = 2.33 \begin {gather*} x+{\left ({\mathrm {e}}^{x^2}\right )}^{1/4}\,{\mathrm {e}}^{3\,x}\,{\mathrm {e}}^{\frac {x^{2\,x}}{x^4}}\,{\mathrm {e}}^9\,{\mathrm {e}}^{\frac {x^x}{x}}\,{\mathrm {e}}^{\frac {6\,x^x}{x^2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________