Optimal. Leaf size=28 \[ -3+\log (2) \left (e^4+x \left (\frac {4}{x}-x+x (4+\log (4))^2\right )\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 14, normalized size of antiderivative = 0.50, number of steps
used = 4, number of rules used = 3, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.136, Rules used = {6, 12, 30}
\begin {gather*} x^2 \log (2) (3+\log (4)) (5+\log (4)) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 6
Rule 12
Rule 30
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (2 x \log (2) \log ^2(4)+x \log (2) (30+16 \log (4))\right ) \, dx\\ &=\int x \log (2) \left (30+16 \log (4)+2 \log ^2(4)\right ) \, dx\\ &=(2 \log (2) (3+\log (4)) (5+\log (4))) \int x \, dx\\ &=x^2 \log (2) (3+\log (4)) (5+\log (4))\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 27, normalized size = 0.96 \begin {gather*} 15 x^2 \log (2)+8 x^2 \log (2) \log (4)+x^2 \log (2) \log ^2(4) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.12, size = 19, normalized size = 0.68
method | result | size |
gosper | \(x^{2} \ln \left (2\right ) \left (4 \ln \left (2\right )^{2}+16 \ln \left (2\right )+15\right )\) | \(19\) |
default | \(x^{2} \ln \left (2\right ) \left (2 \ln \left (2\right )+5\right ) \left (2 \ln \left (2\right )+3\right )\) | \(19\) |
norman | \(\left (4 \ln \left (2\right )^{3}+16 \ln \left (2\right )^{2}+15 \ln \left (2\right )\right ) x^{2}\) | \(22\) |
risch | \(4 x^{2} \ln \left (2\right )^{3}+16 x^{2} \ln \left (2\right )^{2}+15 x^{2} \ln \left (2\right )\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.28, size = 26, normalized size = 0.93 \begin {gather*} 4 \, x^{2} \log \left (2\right )^{3} + 16 \, x^{2} \log \left (2\right )^{2} + 15 \, x^{2} \log \left (2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.33, size = 26, normalized size = 0.93 \begin {gather*} 4 \, x^{2} \log \left (2\right )^{3} + 16 \, x^{2} \log \left (2\right )^{2} + 15 \, x^{2} \log \left (2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.01, size = 20, normalized size = 0.71 \begin {gather*} x^{2} \cdot \left (4 \log {\left (2 \right )}^{3} + 16 \log {\left (2 \right )}^{2} + 15 \log {\left (2 \right )}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.41, size = 26, normalized size = 0.93 \begin {gather*} 4 \, x^{2} \log \left (2\right )^{3} + 16 \, x^{2} \log \left (2\right )^{2} + 15 \, x^{2} \log \left (2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.03, size = 21, normalized size = 0.75 \begin {gather*} x^2\,\left (15\,\ln \left (2\right )+16\,{\ln \left (2\right )}^2+4\,{\ln \left (2\right )}^3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________