Optimal. Leaf size=27 \[ -13+x-x \left (3+\frac {4-x^2}{7+x}+\frac {\log (x)}{x}\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.05, antiderivative size = 18, normalized size of antiderivative = 0.67, number of steps used = 4, number of rules used = 3, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.086, Rules used = {1594, 27, 1620} \begin {gather*} x^2-9 x-\frac {315}{x+7}-\log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 27
Rule 1594
Rule 1620
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-49-140 x-29 x^2+19 x^3+2 x^4}{x \left (49+14 x+x^2\right )} \, dx\\ &=\int \frac {-49-140 x-29 x^2+19 x^3+2 x^4}{x (7+x)^2} \, dx\\ &=\int \left (-9-\frac {1}{x}+2 x+\frac {315}{(7+x)^2}\right ) \, dx\\ &=-9 x+x^2-\frac {315}{7+x}-\log (x)\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 18, normalized size = 0.67 \begin {gather*} -9 x+x^2-\frac {315}{7+x}-\log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.54, size = 26, normalized size = 0.96 \begin {gather*} \frac {x^{3} - 2 \, x^{2} - {\left (x + 7\right )} \log \relax (x) - 63 \, x - 315}{x + 7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.18, size = 19, normalized size = 0.70 \begin {gather*} x^{2} - 9 \, x - \frac {315}{x + 7} - \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.03, size = 19, normalized size = 0.70
method | result | size |
default | \(x^{2}-9 x -\frac {315}{x +7}-\ln \relax (x )\) | \(19\) |
risch | \(x^{2}-9 x -\frac {315}{x +7}-\ln \relax (x )\) | \(19\) |
norman | \(\frac {x^{3}-2 x^{2}+126}{x +7}-\ln \relax (x )\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.36, size = 18, normalized size = 0.67 \begin {gather*} x^{2} - 9 \, x - \frac {315}{x + 7} - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.05, size = 18, normalized size = 0.67 \begin {gather*} x^2-\ln \relax (x)-\frac {315}{x+7}-9\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.09, size = 14, normalized size = 0.52 \begin {gather*} x^{2} - 9 x - \log {\relax (x )} - \frac {315}{x + 7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________