Optimal. Leaf size=19 \[ \frac {5^x x}{\log (5)}-\frac {5^x}{\log ^2(5)} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.400, Rules used = {2176, 2194} \[ \frac {5^x x}{\log (5)}-\frac {5^x}{\log ^2(5)} \]
Antiderivative was successfully verified.
[In]
[Out]
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 = 0.00, size = 14, normalized size = 0.74 \[ \frac {5^x (x \log (5)-1)}{\log ^2(5)} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.42, size = 14, normalized size = 0.74 \[ \frac {{\left (x \log \relax (5) - 1\right )} 5^{x}}{\log \relax (5)^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.86, size = 14, normalized size = 0.74 \[ \frac {{\left (x \log \relax (5) - 1\right )} 5^{x}}{\log \relax (5)^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 15, normalized size = 0.79 \[ \frac {\left (\ln \relax (5) x -1\right ) 5^{x}}{\ln \relax (5)^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.97, size = 14, normalized size = 0.74 \[ \frac {{\left (x \log \relax (5) - 1\right )} 5^{x}}{\log \relax (5)^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.02, size = 14, normalized size = 0.74 \[ \frac {5^x\,\left (x\,\ln \relax (5)-1\right )}{{\ln \relax (5)}^2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.10, size = 14, normalized size = 0.74 \[ \frac {5^{x} \left (x \log {\relax (5 )} - 1\right )}{\log {\relax (5 )}^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________