Optimal. Leaf size=17 \[ \frac {17}{3} \log (3 x+2)-6 \log (x+1) \]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {632, 31} \begin {gather*} \frac {17}{3} \log (3 x+2)-6 \log (x+1) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 31
Rule 632
Rubi steps
\begin {align*} \int \frac {5-x}{2+5 x+3 x^2} \, dx &=17 \int \frac {1}{2+3 x} \, dx-18 \int \frac {1}{3+3 x} \, dx\\ &=-6 \log (1+x)+\frac {17}{3} \log (2+3 x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 17, normalized size = 1.00 \begin {gather*} \frac {17}{3} \log (3 x+2)-6 \log (x+1) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {5-x}{2+5 x+3 x^2} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.38, size = 15, normalized size = 0.88 \begin {gather*} \frac {17}{3} \, \log \left (3 \, x + 2\right ) - 6 \, \log \left (x + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.15, size = 17, normalized size = 1.00 \begin {gather*} \frac {17}{3} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - 6 \, \log \left ({\left | x + 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.05, size = 16, normalized size = 0.94 \begin {gather*} \frac {17 \ln \left (3 x +2\right )}{3}-6 \ln \left (x +1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.73, size = 15, normalized size = 0.88 \begin {gather*} \frac {17}{3} \, \log \left (3 \, x + 2\right ) - 6 \, \log \left (x + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 2.32, size = 13, normalized size = 0.76 \begin {gather*} \frac {17\,\ln \left (x+\frac {2}{3}\right )}{3}-6\,\ln \left (x+1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.10, size = 15, normalized size = 0.88 \begin {gather*} \frac {17 \log {\left (x + \frac {2}{3} \right )}}{3} - 6 \log {\left (x + 1 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________