Optimal. Leaf size=21 \[ e^{5+8 x}-2 x \log \left (\frac {3}{2 x}\right ) \log (x) \]
________________________________________________________________________________________
Rubi [A] time = 0.03, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 4, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.114, Rules used = {2194, 2295, 2361, 12} \begin {gather*} e^{8 x+5}-2 x \log \left (\frac {3}{2 x}\right ) \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 2194
Rule 2295
Rule 2361
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (2 \int \log \left (\frac {3}{2 x}\right ) \, dx\right )+8 \int e^{5+8 x} \, dx+\int \left (2-2 \log \left (\frac {3}{2 x}\right )\right ) \log (x) \, dx\\ &=e^{5+8 x}-2 x-2 x \log \left (\frac {3}{2 x}\right )-2 x \log \left (\frac {3}{2 x}\right ) \log (x)-\int -2 \log \left (\frac {3}{2 x}\right ) \, dx\\ &=e^{5+8 x}-2 x-2 x \log \left (\frac {3}{2 x}\right )-2 x \log \left (\frac {3}{2 x}\right ) \log (x)+2 \int \log \left (\frac {3}{2 x}\right ) \, dx\\ &=e^{5+8 x}-2 x \log \left (\frac {3}{2 x}\right ) \log (x)\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.03, size = 21, normalized size = 1.00 \begin {gather*} e^{5+8 x}-2 x \log \left (\frac {3}{2 x}\right ) \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.54, size = 29, normalized size = 1.38 \begin {gather*} -2 \, x \log \left (\frac {3}{2}\right ) \log \left (\frac {3}{2 \, x}\right ) + 2 \, x \log \left (\frac {3}{2 \, x}\right )^{2} + e^{\left (8 \, x + 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [B] time = 0.19, size = 52, normalized size = 2.48 \begin {gather*} -2 \, x \log \relax (3) \log \relax (x) + 2 \, x \log \relax (2) \log \relax (x) + 2 \, x \log \relax (x)^{2} + 2 \, x \log \relax (3) - 2 \, x \log \relax (2) - 2 \, x \log \relax (x) - 2 \, x \log \left (\frac {3}{2 \, x}\right ) + e^{\left (8 \, x + 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.08, size = 19, normalized size = 0.90
method | result | size |
norman | \({\mathrm e}^{8 x +5}-2 x \ln \left (\frac {3}{2 x}\right ) \ln \relax (x )\) | \(19\) |
risch | \(2 x \ln \relax (x )^{2}-\left (2+2 \ln \relax (3)-2 \ln \relax (2)\right ) x \ln \relax (x )+2 x \ln \relax (3)-2 x \ln \relax (2)-2 x \ln \left (\frac {3}{2 x}\right )+{\mathrm e}^{8 x +5}\) | \(49\) |
default | \(2 x \ln \relax (2) \ln \relax (x )-2 x \ln \relax (2)-2 x \ln \relax (3) \ln \relax (x )+2 x \ln \relax (3)+2 x \ln \left (\frac {1}{x}\right )-2 \ln \relax (x ) \ln \left (\frac {1}{x}\right ) x +{\mathrm e}^{8 x +5}-2 x \ln \left (\frac {3}{2 x}\right )\) | \(57\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.54, size = 18, normalized size = 0.86 \begin {gather*} -2 \, x \log \relax (x) \log \left (\frac {3}{2 \, x}\right ) + e^{\left (8 \, x + 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.18, size = 30, normalized size = 1.43 \begin {gather*} {\mathrm {e}}^{8\,x+5}+2\,x\,\ln \relax (2)\,\ln \relax (x)-2\,x\,\ln \relax (3)\,\ln \relax (x)-2\,x\,\ln \left (\frac {1}{x}\right )\,\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.29, size = 31, normalized size = 1.48 \begin {gather*} 2 x \log {\relax (x )}^{2} + \left (- 2 x \log {\relax (3 )} + 2 x \log {\relax (2 )}\right ) \log {\relax (x )} + e^{8 x + 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________