Optimal. Leaf size=19 \[ \frac{5^x x}{\log (5)}-\frac{5^x}{\log ^2(5)} \]
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Rubi [A] time = 0.0085244, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 5, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.4, Rules used = {2176, 2194} \[ \frac{5^x x}{\log (5)}-\frac{5^x}{\log ^2(5)} \]
Antiderivative was successfully verified.
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Rule 2176
Rule 2194
Rubi steps
\begin{align*} \int 5^x x \, dx &=\frac{5^x x}{\log (5)}-\frac{\int 5^x \, dx}{\log (5)}\\ &=-\frac{5^x}{\log ^2(5)}+\frac{5^x x}{\log (5)}\\ \end{align*}
Mathematica [A] time = 0.0028747, size = 14, normalized size = 0.74 \[ \frac{5^x (x \log (5)-1)}{\log ^2(5)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 15, normalized size = 0.8 \begin{align*}{\frac{ \left ( \ln \left ( 5 \right ) x-1 \right ){5}^{x}}{ \left ( \ln \left ( 5 \right ) \right ) ^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.42486, size = 19, normalized size = 1. \begin{align*} \frac{{\left (x \log \left (5\right ) - 1\right )} 5^{x}}{\log \left (5\right )^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.23962, size = 39, normalized size = 2.05 \begin{align*} \frac{{\left (x \log \left (5\right ) - 1\right )} 5^{x}}{\log \left (5\right )^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.091439, size = 14, normalized size = 0.74 \begin{align*} \frac{5^{x} \left (x \log{\left (5 \right )} - 1\right )}{\log{\left (5 \right )}^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.04894, size = 19, normalized size = 1. \begin{align*} \frac{{\left (x \log \left (5\right ) - 1\right )} 5^{x}}{\log \left (5\right )^{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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