Optimal. Leaf size=20 \[ -5+\frac {2}{e^{5+625 e^{4 x}}+\log (2)} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.08, antiderivative size = 18, normalized size of antiderivative = 0.90, number of steps
used = 4, number of rules used = 4, integrand size = 49, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.082, Rules used = {12, 2320, 2278,
32} \begin {gather*} \frac {2}{e^{625 e^{4 x}+5}+\log (2)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 32
Rule 2278
Rule 2320
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (5000 \int \frac {e^{5+625 e^{4 x}+4 x}}{e^{10+1250 e^{4 x}}+2 e^{5+625 e^{4 x}} \log (2)+\log ^2(2)} \, dx\right )\\ &=-\left (1250 \text {Subst}\left (\int \frac {e^{5+625 x}}{\left (e^{5+625 x}+\log (2)\right )^2} \, dx,x,e^{4 x}\right )\right )\\ &=-\left (2 \text {Subst}\left (\int \frac {1}{(x+\log (2))^2} \, dx,x,e^{5+625 e^{4 x}}\right )\right )\\ &=\frac {2}{e^{5+625 e^{4 x}}+\log (2)}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.03, size = 18, normalized size = 0.90 \begin {gather*} \frac {2}{e^{5+625 e^{4 x}}+\log (2)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.78, size = 17, normalized size = 0.85
method | result | size |
risch | \(\frac {2}{{\mathrm e}^{5+625 \,{\mathrm e}^{4 x}}+\ln \left (2\right )}\) | \(17\) |
norman | \(\frac {2}{{\mathrm e}^{5} {\mathrm e}^{625 \,{\mathrm e}^{4 x}}+\ln \left (2\right )}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.46, size = 16, normalized size = 0.80 \begin {gather*} \frac {2}{e^{\left (625 \, e^{\left (4 \, x\right )} + 5\right )} + \log \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.33, size = 28, normalized size = 1.40 \begin {gather*} \frac {2 \, e^{\left (4 \, x\right )}}{e^{\left (4 \, x\right )} \log \left (2\right ) + e^{\left (4 \, x + 625 \, e^{\left (4 \, x\right )} + 5\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.05, size = 15, normalized size = 0.75 \begin {gather*} \frac {2}{e^{5} e^{625 e^{4 x}} + \log {\left (2 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.39, size = 16, normalized size = 0.80 \begin {gather*} \frac {2}{e^{\left (625 \, e^{\left (4 \, x\right )} + 5\right )} + \log \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 1.00, size = 19, normalized size = 0.95 \begin {gather*} \frac {2\,{\mathrm {e}}^{-5}}{{\mathrm {e}}^{625\,{\mathrm {e}}^{4\,x}}+{\mathrm {e}}^{-5}\,\ln \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________