Optimal. Leaf size=19 \[ x (2+x-25 x (4+x) \log (-9+x)-\log (x)) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.25, antiderivative size = 30, normalized size of antiderivative = 1.58, number of steps
used = 10, number of rules used = 6, integrand size = 48, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {6874, 1864,
45, 2461, 78, 2332} \begin {gather*} -25 x^3 \log (x-9)+x^2-100 x^2 \log (x-9)+2 x-x \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 45
Rule 78
Rule 1864
Rule 2332
Rule 2461
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {-9-17 x-98 x^2-25 x^3+1800 x \log (-9+x)+475 x^2 \log (-9+x)-75 x^3 \log (-9+x)}{-9+x}-\log (x)\right ) \, dx\\ &=\int \frac {-9-17 x-98 x^2-25 x^3+1800 x \log (-9+x)+475 x^2 \log (-9+x)-75 x^3 \log (-9+x)}{-9+x} \, dx-\int \log (x) \, dx\\ &=x-x \log (x)+\int \left (\frac {-9-17 x-98 x^2-25 x^3}{-9+x}-25 x (8+3 x) \log (-9+x)\right ) \, dx\\ &=x-x \log (x)-25 \int x (8+3 x) \log (-9+x) \, dx+\int \frac {-9-17 x-98 x^2-25 x^3}{-9+x} \, dx\\ &=x-100 x^2 \log (-9+x)-25 x^3 \log (-9+x)-x \log (x)+25 \int \frac {(-4-x) x^2}{9-x} \, dx+\int \left (-2924-\frac {26325}{-9+x}-323 x-25 x^2\right ) \, dx\\ &=-2923 x-\frac {323 x^2}{2}-\frac {25 x^3}{3}-26325 \log (9-x)-100 x^2 \log (-9+x)-25 x^3 \log (-9+x)-x \log (x)+25 \int \left (117+\frac {1053}{-9+x}+13 x+x^2\right ) \, dx\\ &=2 x+x^2-100 x^2 \log (-9+x)-25 x^3 \log (-9+x)-x \log (x)\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.04, size = 30, normalized size = 1.58 \begin {gather*} 2 x+x^2-100 x^2 \log (-9+x)-25 x^3 \log (-9+x)-x \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. \(50\) vs.
\(2(19)=38\).
time = 0.29, size = 51, normalized size = 2.68
method | result | size |
risch | \(\left (-25 x^{3}-100 x^{2}\right ) \ln \left (x -9\right )+x^{2}-x \ln \left (x \right )+2 x\) | \(29\) |
default | \(x^{2}+2 x -26325 \ln \left (x -9\right )-25 \left (x -9\right )^{3} \ln \left (x -9\right )-\frac {91125}{2}-775 \left (x -9\right )^{2} \ln \left (x -9\right )-7875 \ln \left (x -9\right ) \left (x -9\right )-x \ln \left (x \right )\) | \(51\) |
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. 71 vs.
\(2 (20) = 40\).
time = 0.30, size = 71, normalized size = 3.74 \begin {gather*} x^{2} - \frac {25}{2} \, {\left (2 \, x^{3} + 27 \, x^{2} + 486 \, x + 4374 \, \log \left (x - 9\right )\right )} \log \left (x - 9\right ) + \frac {475}{2} \, {\left (x^{2} + 18 \, x + 162 \, \log \left (x - 9\right )\right )} \log \left (x - 9\right ) + 1800 \, {\left (x + 9 \, \log \left (x - 9\right )\right )} \log \left (x - 9\right ) - x \log \left (x\right ) + 2 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.48, size = 27, normalized size = 1.42 \begin {gather*} x^{2} - 25 \, {\left (x^{3} + 4 \, x^{2}\right )} \log \left (x - 9\right ) - x \log \left (x\right ) + 2 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.25, size = 37, normalized size = 1.95 \begin {gather*} x^{2} - x \log {\left (x \right )} + 2 x + \left (- 25 x^{3} - 100 x^{2} + \frac {29025}{4}\right ) \log {\left (x - 9 \right )} - \frac {29025 \log {\left (x - 9 \right )}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.39, size = 27, normalized size = 1.42 \begin {gather*} x^{2} - 25 \, {\left (x^{3} + 4 \, x^{2}\right )} \log \left (x - 9\right ) - x \log \left (x\right ) + 2 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 1.88, size = 29, normalized size = 1.53 \begin {gather*} 2\,x-\ln \left (x-9\right )\,\left (25\,x^3+100\,x^2\right )-x\,\ln \left (x\right )+x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________