Optimal. Leaf size=20 \[ 5 \left (4-x+x^4 \log ^2(4)\right )+\log \left (x^2\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.00, antiderivative size = 17, normalized size of antiderivative = 0.85, number of steps
used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {14}
\begin {gather*} 5 x^4 \log ^2(4)-5 x+2 \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-5+\frac {2}{x}+20 x^3 \log ^2(4)\right ) \, dx\\ &=-5 x+5 x^4 \log ^2(4)+2 \log (x)\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 17, normalized size = 0.85 \begin {gather*} -5 x+5 x^4 \log ^2(4)+2 \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.25, size = 18, normalized size = 0.90
method | result | size |
default | \(-5 x +20 x^{4} \ln \left (2\right )^{2}+2 \ln \left (x \right )\) | \(18\) |
norman | \(-5 x +20 x^{4} \ln \left (2\right )^{2}+2 \ln \left (x \right )\) | \(18\) |
risch | \(-5 x +20 x^{4} \ln \left (2\right )^{2}+2 \ln \left (x \right )\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.26, size = 17, normalized size = 0.85 \begin {gather*} 20 \, x^{4} \log \left (2\right )^{2} - 5 \, x + 2 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.41, size = 17, normalized size = 0.85 \begin {gather*} 20 \, x^{4} \log \left (2\right )^{2} - 5 \, x + 2 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.02, size = 17, normalized size = 0.85 \begin {gather*} 20 x^{4} \log {\left (2 \right )}^{2} - 5 x + 2 \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.42, size = 18, normalized size = 0.90 \begin {gather*} 20 \, x^{4} \log \left (2\right )^{2} - 5 \, x + 2 \, \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.03, size = 17, normalized size = 0.85 \begin {gather*} 2\,\ln \left (x\right )-5\,x+20\,x^4\,{\ln \left (2\right )}^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________