Optimal. Leaf size=25 \[ \frac {3 e^{-5+\left (-4+e^{10}\right ) (-2+x) x+x^2}}{x+\log (3)} \]
[Out]
________________________________________________________________________________________
Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(90\) vs. \(2(25)=50\).
time = 0.40, antiderivative size = 90, normalized size of antiderivative = 3.60, number of steps
used = 2, number of rules used = 2, integrand size = 82, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.024, Rules used = {27, 2326}
\begin {gather*} \frac {3 e^{-3 x^2-e^{10} \left (2 x-x^2\right )+8 x-5} \left (-3 x^2-e^{10} \left (x-x^2\right )+4 x+\left (-e^{10} (1-x)-3 x+4\right ) \log (3)\right )}{\left (-e^{10} (1-x)-3 x+4\right ) (x+\log (3))^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 27
Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{-5+8 x-3 x^2-e^{10} \left (2 x-x^2\right )} \left (-3+24 x-18 x^2+e^{10} \left (-6 x+6 x^2\right )+\left (24-18 x+e^{10} (-6+6 x)\right ) \log (3)\right )}{(x+\log (3))^2} \, dx\\ &=\frac {3 e^{-5+8 x-3 x^2-e^{10} \left (2 x-x^2\right )} \left (4 x-3 x^2-e^{10} \left (x-x^2\right )+\left (4-e^{10} (1-x)-3 x\right ) \log (3)\right )}{\left (4-e^{10} (1-x)-3 x\right ) (x+\log (3))^2}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(85\) vs. \(2(25)=50\).
time = 0.24, size = 85, normalized size = 3.40 \begin {gather*} \frac {3 e^{-5+8 x+e^{10} (-2+x) x-3 x^2} \left (2 \left (-3+e^{10}\right ) x^2+8 \log (3)+x \left (8-6 \log (3)+e^{10} (-2+\log (9))\right )-e^{10} \log (9)\right )}{\left (8+e^{10} (-2+x)-6 x+e^{10} x\right ) (x+\log (3))^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 3.63, size = 31, normalized size = 1.24
method | result | size |
risch | \(\frac {3 \,{\mathrm e}^{{\mathrm e}^{10} x^{2}-2 x \,{\mathrm e}^{10}-3 x^{2}+8 x -5}}{\ln \left (3\right )+x}\) | \(31\) |
norman | \(\frac {3 \,{\mathrm e}^{-\left (-x^{2}+2 x \right ) {\mathrm e}^{10}-3 x^{2}+8 x -5}}{\ln \left (3\right )+x}\) | \(36\) |
gosper | \(\frac {3 \,{\mathrm e}^{{\mathrm e}^{10} x^{2}-2 x \,{\mathrm e}^{10}-3 x^{2}+8 x -5}}{\ln \left (3\right )+x}\) | \(38\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.57, size = 35, normalized size = 1.40 \begin {gather*} \frac {3 \, e^{\left (x^{2} e^{10} - 3 \, x^{2} - 2 \, x e^{10} + 8 \, x\right )}}{x e^{5} + e^{5} \log \left (3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.43, size = 29, normalized size = 1.16 \begin {gather*} \frac {3 \, e^{\left (-3 \, x^{2} + {\left (x^{2} - 2 \, x\right )} e^{10} + 8 \, x - 5\right )}}{x + \log \left (3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.13, size = 27, normalized size = 1.08 \begin {gather*} \frac {3 e^{- 3 x^{2} + 8 x - \left (- x^{2} + 2 x\right ) e^{10} - 5}}{x + \log {\left (3 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 8.81, size = 33, normalized size = 1.32 \begin {gather*} \frac {3\,{\mathrm {e}}^{x^2\,{\mathrm {e}}^{10}}\,{\mathrm {e}}^{8\,x}\,{\mathrm {e}}^{-5}\,{\mathrm {e}}^{-3\,x^2}\,{\mathrm {e}}^{-2\,x\,{\mathrm {e}}^{10}}}{x+\ln \left (3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________