Optimal. Leaf size=14 \[ \frac {5}{-1+e^{x (1+\log (16))}} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.05, antiderivative size = 13, normalized size of antiderivative = 0.93, number of steps
used = 3, number of rules used = 3, integrand size = 40, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.075, Rules used = {12, 2320, 32}
\begin {gather*} -\frac {5}{1-(16 e)^x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 32
Rule 2320
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left ((5 (1+\log (16))) \int \frac {e^{x+x \log (16)}}{1-2 e^{x+x \log (16)}+e^{2 x+2 x \log (16)}} \, dx\right )\\ &=-\left (5 \text {Subst}\left (\int \frac {1}{(1-x)^2} \, dx,x,e^{x (1+\log (16))}\right )\right )\\ &=-\frac {5}{1-(16 e)^x}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.07, size = 21, normalized size = 1.50 \begin {gather*} \frac {5 (1+\log (16))}{\left (-1+(16 e)^x\right ) \log (16 e)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.42, size = 29, normalized size = 2.07
method | result | size |
norman | \(\frac {5}{{\mathrm e}^{4 x \ln \left (2\right )+x}-1}\) | \(15\) |
derivativedivides | \(-\frac {5 \left (-4 \ln \left (2\right )-1\right )}{\left (1+4 \ln \left (2\right )\right ) \left ({\mathrm e}^{4 x \ln \left (2\right )+x}-1\right )}\) | \(29\) |
default | \(-\frac {-20 \ln \left (2\right )-5}{\left (1+4 \ln \left (2\right )\right ) \left ({\mathrm e}^{4 x \ln \left (2\right )+x}-1\right )}\) | \(29\) |
risch | \(\frac {20 \ln \left (2\right )}{\left (1+4 \ln \left (2\right )\right ) \left (16^{x} {\mathrm e}^{x}-1\right )}+\frac {5}{\left (1+4 \ln \left (2\right )\right ) \left (16^{x} {\mathrm e}^{x}-1\right )}\) | \(44\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.54, size = 14, normalized size = 1.00 \begin {gather*} \frac {5}{e^{\left (4 \, x \log \left (2\right ) + x\right )} - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.36, size = 14, normalized size = 1.00 \begin {gather*} \frac {5}{e^{\left (4 \, x \log \left (2\right ) + x\right )} - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.03, size = 12, normalized size = 0.86 \begin {gather*} \frac {5}{e^{x + 4 x \log {\left (2 \right )}} - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.42, size = 15, normalized size = 1.07 \begin {gather*} \frac {5}{e^{\left (x {\left (4 \, \log \left (2\right ) + 1\right )}\right )} - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 4.64, size = 144, normalized size = 10.29 \begin {gather*} \frac {10\,\mathrm {atan}\left (\frac {\ln \left (256\right )+2}{\sqrt {4\,{\ln \left (16\right )}^2-{\ln \left (256\right )}^2}}-\frac {2^{4\,x}\,{\mathrm {e}}^x\,\left (\ln \left (256\right )+2\right )}{\sqrt {4\,{\ln \left (16\right )}^2-{\ln \left (256\right )}^2}}\right )}{\sqrt {4\,{\ln \left (16\right )}^2-{\ln \left (256\right )}^2}}+\frac {40\,\ln \left (2\right )\,\mathrm {atan}\left (\frac {\ln \left (256\right )-2\,2^{4\,x}\,{\mathrm {e}}^x-2\,2^{4\,x}\,{\mathrm {e}}^x\,\ln \left (16\right )+2}{\sqrt {8\,\ln \left (16\right )-4\,\ln \left (256\right )+4\,{\ln \left (16\right )}^2-{\ln \left (256\right )}^2}}\right )}{\sqrt {8\,\ln \left (16\right )-4\,\ln \left (256\right )+4\,{\ln \left (16\right )}^2-{\ln \left (256\right )}^2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________