Optimal. Leaf size=24 \[ \frac {x^3}{6}-\frac {3 x^2}{4}+4 x-12 \log (x+3) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 24, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {1593, 772} \[ \frac {x^3}{6}-\frac {3 x^2}{4}+4 x-12 \log (x+3) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 772
Rule 1593
Rubi steps
\begin {align*} \int \frac {-x+x^3}{6+2 x} \, dx &=\int \frac {x \left (-1+x^2\right )}{6+2 x} \, dx\\ &=\int \left (4-\frac {3 x}{2}+\frac {x^2}{2}-\frac {12}{3+x}\right ) \, dx\\ &=4 x-\frac {3 x^2}{4}+\frac {x^3}{6}-12 \log (3+x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 31, normalized size = 1.29 \[ \frac {1}{2} \left (\frac {x^3}{3}-\frac {3 x^2}{2}+8 x-24 \log (x+3)+\frac {93}{2}\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.55, size = 20, normalized size = 0.83 \[ \frac {1}{6} \, x^{3} - \frac {3}{4} \, x^{2} + 4 \, x - 12 \, \log \left (x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.31, size = 21, normalized size = 0.88 \[ \frac {1}{6} \, x^{3} - \frac {3}{4} \, x^{2} + 4 \, x - 12 \, \log \left ({\left | x + 3 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 21, normalized size = 0.88 \[ \frac {x^{3}}{6}-\frac {3 x^{2}}{4}+4 x -12 \ln \left (x +3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.63, size = 20, normalized size = 0.83 \[ \frac {1}{6} \, x^{3} - \frac {3}{4} \, x^{2} + 4 \, x - 12 \, \log \left (x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.04, size = 20, normalized size = 0.83 \[ 4\,x-12\,\ln \left (x+3\right )-\frac {3\,x^2}{4}+\frac {x^3}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.08, size = 20, normalized size = 0.83 \[ \frac {x^{3}}{6} - \frac {3 x^{2}}{4} + 4 x - 12 \log {\left (x + 3 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________