Optimal. Leaf size=16 \[ 5 (4+3 x) (1+x-\log (2)) \log (x) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.03, antiderivative size = 29, normalized size of antiderivative = 1.81, number of steps
used = 6, number of rules used = 3, integrand size = 39, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {14, 77, 2350}
\begin {gather*} 15 x^2 \log (x)+5 x (7-\log (8)) \log (x)+20 (1-\log (2)) \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 14
Rule 77
Rule 2350
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {5 (4+3 x) (1+x-\log (2))}{x}+5 (7+6 x-\log (8)) \log (x)\right ) \, dx\\ &=5 \int \frac {(4+3 x) (1+x-\log (2))}{x} \, dx+5 \int (7+6 x-\log (8)) \log (x) \, dx\\ &=5 \left (3 x^2+x (7-\log (8))\right ) \log (x)-5 \int (7+3 x-\log (8)) \, dx+5 \int \left (7+3 x-\frac {4 (-1+\log (2))}{x}-\log (8)\right ) \, dx\\ &=20 (1-\log (2)) \log (x)+5 \left (3 x^2+x (7-\log (8))\right ) \log (x)\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(40\) vs. \(2(16)=32\).
time = 0.02, size = 40, normalized size = 2.50 \begin {gather*} -15 x \log (2)+5 x \log (8)+20 \log (x)+35 x \log (x)+15 x^2 \log (x)-20 \log (2) \log (x)-5 x \log (8) \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(40\) vs.
\(2(15)=30\).
time = 0.45, size = 41, normalized size = 2.56
method | result | size |
norman | \(\left (-20 \ln \left (2\right )+20\right ) \ln \left (x \right )+\left (-15 \ln \left (2\right )+35\right ) x \ln \left (x \right )+15 x^{2} \ln \left (x \right )\) | \(28\) |
risch | \(\left (-15 x \ln \left (2\right )+15 x^{2}+35 x \right ) \ln \left (x \right )-20 \ln \left (2\right ) \ln \left (x \right )+20 \ln \left (x \right )\) | \(29\) |
default | \(-15 \ln \left (2\right ) \left (x \ln \left (x \right )-x \right )+15 x^{2} \ln \left (x \right )+35 x \ln \left (x \right )-15 x \ln \left (2\right )-20 \ln \left (2\right ) \ln \left (x \right )+20 \ln \left (x \right )\) | \(41\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 40 vs.
\(2 (16) = 32\).
time = 0.27, size = 40, normalized size = 2.50 \begin {gather*} 15 \, x^{2} \log \left (x\right ) - 15 \, {\left (x \log \left (x\right ) - x\right )} \log \left (2\right ) - 15 \, x \log \left (2\right ) + 35 \, x \log \left (x\right ) - 20 \, \log \left (2\right ) \log \left (x\right ) + 20 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.38, size = 23, normalized size = 1.44 \begin {gather*} 5 \, {\left (3 \, x^{2} - {\left (3 \, x + 4\right )} \log \left (2\right ) + 7 \, x + 4\right )} \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.06, size = 27, normalized size = 1.69 \begin {gather*} \left (15 x^{2} - 15 x \log {\left (2 \right )} + 35 x\right ) \log {\left (x \right )} + \left (20 - 20 \log {\left (2 \right )}\right ) \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.38, size = 28, normalized size = 1.75 \begin {gather*} 5 \, {\left (3 \, x^{2} - x {\left (3 \, \log \left (2\right ) - 7\right )}\right )} \log \left (x\right ) - 20 \, {\left (\log \left (2\right ) - 1\right )} \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 4.26, size = 16, normalized size = 1.00 \begin {gather*} 5\,\ln \left (x\right )\,\left (3\,x+4\right )\,\left (x-\ln \left (2\right )+1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________