Optimal. Leaf size=12 \[ 2^{-x+9 \log (9+x)} \]
________________________________________________________________________________________
Rubi [A] time = 0.11, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.115, Rules used = {12, 2274, 2197} \begin {gather*} 2^{-x} (x+9)^{\log (512)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 2197
Rule 2274
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (\log (2) \int \frac {e^{-x \log (2)+9 \log (2) \log (9+x)} x}{9+x} \, dx\right )\\ &=-\left (\log (2) \int 2^{-x} x (9+x)^{-1+9 \log (2)} \, dx\right )\\ &=2^{-x} (9+x)^{\log (512)}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.05, size = 12, normalized size = 1.00 \begin {gather*} 2^{-x+9 \log (9+x)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.81, size = 15, normalized size = 1.25 \begin {gather*} e^{\left (-x \log \relax (2) + 9 \, \log \relax (2) \log \left (x + 9\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.19, size = 15, normalized size = 1.25 \begin {gather*} e^{\left (-x \log \relax (2) + 9 \, \log \relax (2) \log \left (x + 9\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.36, size = 13, normalized size = 1.08
method | result | size |
risch | \(\left (x +9\right )^{9 \ln \relax (2)} \left (\frac {1}{2}\right )^{x}\) | \(13\) |
gosper | \({\mathrm e}^{9 \ln \relax (2) \ln \left (x +9\right )-x \ln \relax (2)}\) | \(16\) |
norman | \({\mathrm e}^{9 \ln \relax (2) \ln \left (x +9\right )-x \ln \relax (2)}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.43, size = 15, normalized size = 1.25 \begin {gather*} e^{\left (-x \log \relax (2) + 9 \, \log \relax (2) \log \left (x + 9\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.23, size = 14, normalized size = 1.17 \begin {gather*} \frac {{\left (x+9\right )}^{9\,\ln \relax (2)}}{2^x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.30, size = 15, normalized size = 1.25 \begin {gather*} e^{- x \log {\relax (2 )} + 9 \log {\relax (2 )} \log {\left (x + 9 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________