Optimal. Leaf size=20 \[ 3 x \left (x-x^2-\log (5 (4-x))\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.07, antiderivative size = 34, normalized size of antiderivative = 1.70, number of steps
used = 6, number of rules used = 4, integrand size = 32, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {6874, 785,
2436, 2332} \begin {gather*} -3 x^3+3 x^2-12 \log (4-x)+3 (4-x) \log (5 (4-x)) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 785
Rule 2332
Rule 2436
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {3 x \left (9-14 x+3 x^2\right )}{-4+x}-3 \log (20-5 x)\right ) \, dx\\ &=-\left (3 \int \frac {x \left (9-14 x+3 x^2\right )}{-4+x} \, dx\right )-3 \int \log (20-5 x) \, dx\\ &=\frac {3}{5} \text {Subst}(\int \log (x) \, dx,x,20-5 x)-3 \int \left (1+\frac {4}{-4+x}-2 x+3 x^2\right ) \, dx\\ &=3 x^2-3 x^3-12 \log (4-x)+3 (4-x) \log (5 (4-x))\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 40, normalized size = 2.00 \begin {gather*} -123 (-4+x)-33 (-4+x)^2-3 (-4+x)^3+3 x-3 (-4+x) \log (-5 (-4+x))-12 \log (-4+x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(44\) vs.
\(2(19)=38\).
time = 0.62, size = 45, normalized size = 2.25
method | result | size |
norman | \(3 x^{2}-3 x^{3}-3 \ln \left (-5 x +20\right ) x\) | \(21\) |
risch | \(3 x^{2}-3 x^{3}-3 \ln \left (-5 x +20\right ) x\) | \(21\) |
derivativedivides | \(\frac {3 \left (-5 x +20\right )^{3}}{125}+\frac {3 \ln \left (-5 x +20\right ) \left (-5 x +20\right )}{5}-120 x +480-\frac {33 \left (-5 x +20\right )^{2}}{25}-12 \ln \left (-5 x +20\right )\) | \(45\) |
default | \(\frac {3 \left (-5 x +20\right )^{3}}{125}+\frac {3 \ln \left (-5 x +20\right ) \left (-5 x +20\right )}{5}-120 x +480-\frac {33 \left (-5 x +20\right )^{2}}{25}-12 \ln \left (-5 x +20\right )\) | \(45\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [C] Result contains complex when optimal does not.
time = 0.51, size = 49, normalized size = 2.45 \begin {gather*} -3 \, x^{3} + 3 \, x^{2} - 12 \, {\left (-i \, \pi - \log \left (5\right )\right )} \log \left (x - 4\right ) + 12 \, \log \left (x - 4\right )^{2} - 3 \, {\left (x + 4 \, \log \left (x - 4\right )\right )} \log \left (-5 \, x + 20\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.37, size = 20, normalized size = 1.00 \begin {gather*} -3 \, x^{3} + 3 \, x^{2} - 3 \, x \log \left (-5 \, x + 20\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.04, size = 19, normalized size = 0.95 \begin {gather*} - 3 x^{3} + 3 x^{2} - 3 x \log {\left (20 - 5 x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.41, size = 20, normalized size = 1.00 \begin {gather*} -3 \, x^{3} + 3 \, x^{2} - 3 \, x \log \left (-5 \, x + 20\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.11, size = 16, normalized size = 0.80 \begin {gather*} -3\,x\,\left (\ln \left (20-5\,x\right )-x+x^2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________