Optimal. Leaf size=33 \[ -\frac {3^{2^x}}{\log (2) \log ^2(3)}+\frac {2^x 3^{2^x}}{\log (2) \log (3)} \]
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Rubi [A]
time = 0.02, antiderivative size = 33, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 3, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.333, Rules used = {2320, 2207,
2225} \begin {gather*} \frac {2^x 3^{2^x}}{\log (2) \log (3)}-\frac {3^{2^x}}{\log (2) \log ^2(3)} \end {gather*}
Antiderivative was successfully verified.
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Rule 2207
Rule 2225
Rule 2320
Rubi steps
\begin {gather*} \begin {aligned} \text {Integral} &=\frac {\text {Subst}\left (\int 3^x x \, dx,x,2^x\right )}{\log (2)}\\ &=\frac {2^x 3^{2^x}}{\log (2) \log (3)}-\frac {\text {Subst}\left (\int 3^x \, dx,x,2^x\right )}{\log (2) \log (3)}\\ &=-\frac {3^{2^x}}{\log (2) \log ^2(3)}+\frac {2^x 3^{2^x}}{\log (2) \log (3)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 22, normalized size = 0.67 \begin {gather*} \frac {3^{2^x} \left (-1+2^x \log (3)\right )}{\log (2) \log ^2(3)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.06, size = 23, normalized size = 0.70
method | result | size |
risch | \(\frac {\left (2^{x} \ln \left (3\right )-1\right ) 3^{2^{x}}}{\ln \left (2\right ) \ln \left (3\right )^{2}}\) | \(23\) |
norman | \(\frac {{\mathrm e}^{x \ln \left (2\right )} {\mathrm e}^{{\mathrm e}^{x \ln \left (2\right )} \ln \left (3\right )}}{\ln \left (2\right ) \ln \left (3\right )}-\frac {{\mathrm e}^{{\mathrm e}^{x \ln \left (2\right )} \ln \left (3\right )}}{\ln \left (2\right ) \ln \left (3\right )^{2}}\) | \(44\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [C] Result contains higher order function than in optimal. Order 4 vs. order
3.
time = 0.45, size = 31, normalized size = 0.94 \begin {gather*} -\frac {4^{x} \Gamma \left (2, -4^{\frac {1}{2} \, x} \log \left (3\right )\right )}{4^{x} \log \left (3\right )^{2} \log \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.57, size = 22, normalized size = 0.67 \begin {gather*} \frac {{\left (2^{x} \log \left (3\right ) - 1\right )} 3^{\left (2^{x}\right )}}{\log \left (3\right )^{2} \log \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 24, normalized size = 0.73 \begin {gather*} \frac {\left (2^{x} \log {\left (3 \right )} - 1\right ) e^{2^{x} \log {\left (3 \right )}}}{\log {\left (2 \right )} \log {\left (3 \right )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.46, size = 51, normalized size = 1.55 \begin {gather*} \frac {2^{x} e^{\left (2^{x} \log \left (3\right ) + 2 \, x \log \left (2\right )\right )} \log \left (3\right ) - e^{\left (2^{x} \log \left (3\right ) + 2 \, x \log \left (2\right )\right )}}{2^{2 \, x} \log \left (3\right )^{2} \log \left (2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.14, size = 22, normalized size = 0.67 \begin {gather*} \frac {3^{2^x}\,\left (2^x\,\ln \left (3\right )-1\right )}{\ln \left (2\right )\,{\ln \left (3\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Chatgpt [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {not solved} \end {gather*}
Warning: Unable to verify antiderivative.
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