Optimal. Leaf size=17 \[ \frac {1}{\sqrt [35]{e} \left (5-e^x\right )}+x \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.05, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps
used = 4, number of rules used = 3, integrand size = 59, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.051, Rules used = {2320, 12, 907}
\begin {gather*} x+\frac {1}{\sqrt [35]{e} \left (5-e^x\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 907
Rule 2320
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\text {Subst}\left (\int \frac {25 \sqrt [35]{e}+\left (1-10 \sqrt [35]{e}\right ) x+\sqrt [35]{e} x^2}{\sqrt [35]{e} (5-x)^2 x} \, dx,x,e^x\right )\\ &=\frac {\text {Subst}\left (\int \frac {25 \sqrt [35]{e}+\left (1-10 \sqrt [35]{e}\right ) x+\sqrt [35]{e} x^2}{(5-x)^2 x} \, dx,x,e^x\right )}{\sqrt [35]{e}}\\ &=\frac {\text {Subst}\left (\int \left (\frac {1}{(-5+x)^2}+\frac {\sqrt [35]{e}}{x}\right ) \, dx,x,e^x\right )}{\sqrt [35]{e}}\\ &=\frac {1}{\sqrt [35]{e} \left (5-e^x\right )}+x\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.11, size = 25, normalized size = 1.47 \begin {gather*} \frac {\frac {1}{\sqrt [35]{e}}+5 x-e^x x}{5-e^x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.41, size = 21, normalized size = 1.24
method | result | size |
risch | \(x -\frac {{\mathrm e}^{-\frac {1}{35}}}{{\mathrm e}^{x}-5}\) | \(13\) |
derivativedivides | \({\mathrm e}^{-\frac {1}{35}} \left (-\frac {1}{{\mathrm e}^{x}-5}+{\mathrm e}^{\frac {1}{35}} \ln \left ({\mathrm e}^{x}\right )\right )\) | \(21\) |
default | \({\mathrm e}^{-\frac {1}{35}} \left (-\frac {1}{{\mathrm e}^{x}-5}+{\mathrm e}^{\frac {1}{35}} \ln \left ({\mathrm e}^{x}\right )\right )\) | \(21\) |
norman | \(\frac {{\mathrm e}^{x} x -5 x -{\mathrm e}^{-\frac {1}{35}}}{{\mathrm e}^{x}-5}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.27, size = 15, normalized size = 0.88 \begin {gather*} x + \frac {1}{5 \, e^{\frac {1}{35}} - e^{\left (x + \frac {1}{35}\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. 28 vs.
\(2 (12) = 24\).
time = 0.38, size = 28, normalized size = 1.65 \begin {gather*} \frac {5 \, x e^{\frac {1}{35}} - x e^{\left (x + \frac {1}{35}\right )} + 1}{5 \, e^{\frac {1}{35}} - e^{\left (x + \frac {1}{35}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.03, size = 17, normalized size = 1.00 \begin {gather*} x - \frac {1}{e^{\frac {1}{35}} e^{x} - 5 e^{\frac {1}{35}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.40, size = 12, normalized size = 0.71 \begin {gather*} x - \frac {e^{\left (-\frac {1}{35}\right )}}{e^{x} - 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 4.31, size = 15, normalized size = 0.88 \begin {gather*} x-\frac {1}{{\mathrm {e}}^{x+\frac {1}{35}}-5\,{\mathrm {e}}^{1/35}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________