Optimal. Leaf size=33 \[ \frac {e^{6+2 x^2+2 x \left (-e^x-x+\log (25-x)\right )} \log (2)}{x^2} \]
[Out]
________________________________________________________________________________________
Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(102\) vs. \(2(33)=66\).
time = 5.10, antiderivative size = 102, normalized size of antiderivative = 3.09, number of steps
used = 4, number of rules used = 4, integrand size = 83, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {1607, 6873, 12,
2326} \begin {gather*} \frac {e^{2 \left (3-e^x x\right )} (25-x)^{2 x-1} \log (2) \left (-e^x x^3+24 e^x x^2+x^2+x^2 \log (25-x)+25 e^x x-25 x \log (25-x)\right )}{x^3 \left (e^x x+\frac {x}{25-x}+e^x-\log (25-x)\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 1607
Rule 2326
Rule 6873
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{6-2 e^x x+2 x \log (25-x)} \left (\left (50-2 x+2 x^2\right ) \log (2)+e^x \left (50 x+48 x^2-2 x^3\right ) \log (2)+\left (-50 x+2 x^2\right ) \log (2) \log (25-x)\right )}{(-25+x) x^3} \, dx\\ &=\int \frac {2 e^{-2 \left (-3+e^x x-x \log (25-x)\right )} \log (2) \left (-25+x-25 e^x x-x^2-24 e^x x^2+e^x x^3+25 x \log (25-x)-x^2 \log (25-x)\right )}{(25-x) x^3} \, dx\\ &=(2 \log (2)) \int \frac {e^{-2 \left (-3+e^x x-x \log (25-x)\right )} \left (-25+x-25 e^x x-x^2-24 e^x x^2+e^x x^3+25 x \log (25-x)-x^2 \log (25-x)\right )}{(25-x) x^3} \, dx\\ &=\frac {e^{2 \left (3-e^x x\right )} (25-x)^{-1+2 x} \log (2) \left (25 e^x x+x^2+24 e^x x^2-e^x x^3-25 x \log (25-x)+x^2 \log (25-x)\right )}{x^3 \left (e^x+e^x x+\frac {x}{25-x}-\log (25-x)\right )}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 1.42, size = 25, normalized size = 0.76 \begin {gather*} \frac {e^{6-2 e^x x} (25-x)^{2 x} \log (2)}{x^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.39, size = 24, normalized size = 0.73
method | result | size |
risch | \(\frac {\ln \left (2\right ) \left (-x +25\right )^{2 x} {\mathrm e}^{-2 \,{\mathrm e}^{x} x +6}}{x^{2}}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.67, size = 23, normalized size = 0.70 \begin {gather*} \frac {e^{\left (-2 \, x e^{x} + 2 \, x \log \left (-x + 25\right ) + 6\right )} \log \left (2\right )}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.30, size = 23, normalized size = 0.70 \begin {gather*} \frac {e^{\left (-2 \, x e^{x} + 2 \, x \log \left (-x + 25\right ) + 6\right )} \log \left (2\right )}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.18, size = 24, normalized size = 0.73 \begin {gather*} \frac {e^{- 2 x e^{x} + 2 x \log {\left (25 - x \right )} + 6} \log {\left (2 \right )}}{x^{2}} \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 = 0.79, size = 23, normalized size = 0.70 \begin {gather*} \frac {{\mathrm {e}}^{-2\,x\,{\mathrm {e}}^x}\,{\mathrm {e}}^6\,\ln \left (2\right )\,{\left (25-x\right )}^{2\,x}}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________