Optimal. Leaf size=20 \[ \frac {(7 x-8)^{1+\log (2)}}{7 (1+\log (2))} \]
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Rubi [A] time = 0.00, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {2274, 32} \[ \frac {(7 x-8)^{1+\log (2)}}{7 (1+\log (2))} \]
Antiderivative was successfully verified.
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Rule 32
Rule 2274
Rubi steps
\begin {align*} \int 2^{\log (-8+7 x)} \, dx &=\int (-8+7 x)^{\log (2)} \, dx\\ &=\frac {(-8+7 x)^{1+\log (2)}}{7 (1+\log (2))}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 20, normalized size = 1.00 \[ \frac {(7 x-8) 2^{\log (7 x-8)}}{7+\log (128)} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.44, size = 23, normalized size = 1.15 \[ \frac {{\left (7 \, x - 8\right )} e^{\left (\log \relax (2) \log \left (7 \, x - 8\right )\right )}}{7 \, {\left (\log \relax (2) + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 23, normalized size = 1.15 \[ \frac {{\left (7 \, x - 8\right )} e^{\left (\log \relax (2) \log \left (7 \, x - 8\right )\right )}}{7 \, {\left (\log \relax (2) + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 22, normalized size = 1.10 \[ \frac {\left (7 x -8\right ) 2^{\ln \left (7 x -8\right )}}{7 \ln \relax (2)+7} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.59, size = 29, normalized size = 1.45 \[ \frac {2^{{\left (\frac {1}{\log \relax (2)} + 1\right )} \log \left (7 \, x - 8\right )}}{7 \, {\left (\frac {1}{\log \relax (2)} + 1\right )} \log \relax (2)} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.39, size = 19, normalized size = 0.95 \[ \frac {{\left (7\,x-8\right )}^{\ln \relax (2)+1}}{7\,\left (\ln \relax (2)+1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.49, size = 34, normalized size = 1.70 \[ \frac {7 \cdot 2^{\log {\left (7 x - 8 \right )}} x}{7 \log {\relax (2 )} + 7} - \frac {8 \cdot 2^{\log {\left (7 x - 8 \right )}}}{7 \log {\relax (2 )} + 7} \]
Verification of antiderivative is not currently implemented for this CAS.
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