Optimal. Leaf size=14 \[ \frac {1}{x}+2 \log (x)+3 \log (x+2) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {1593, 893} \[ \frac {1}{x}+2 \log (x)+3 \log (x+2) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 893
Rule 1593
Rubi steps
\begin {align*} \int \frac {-2+3 x+5 x^2}{2 x^2+x^3} \, dx &=\int \frac {-2+3 x+5 x^2}{x^2 (2+x)} \, dx\\ &=\int \left (-\frac {1}{x^2}+\frac {2}{x}+\frac {3}{2+x}\right ) \, dx\\ &=\frac {1}{x}+2 \log (x)+3 \log (2+x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 14, normalized size = 1.00 \[ \frac {1}{x}+2 \log (x)+3 \log (x+2) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.77, size = 18, normalized size = 1.29 \[ \frac {3 \, x \log \left (x + 2\right ) + 2 \, x \log \relax (x) + 1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.37, size = 16, normalized size = 1.14 \[ \frac {1}{x} + 3 \, \log \left ({\left | x + 2 \right |}\right ) + 2 \, \log \left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 15, normalized size = 1.07 \[ 2 \ln \relax (x )+3 \ln \left (x +2\right )+\frac {1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.00, size = 14, normalized size = 1.00 \[ \frac {1}{x} + 3 \, \log \left (x + 2\right ) + 2 \, \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 2.12, size = 14, normalized size = 1.00 \[ 3\,\ln \left (x+2\right )+2\,\ln \relax (x)+\frac {1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.12, size = 14, normalized size = 1.00 \[ 2 \log {\relax (x )} + 3 \log {\left (x + 2 \right )} + \frac {1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________