Optimal. Leaf size=19 \[ \frac {7}{11} \log (3-2 x)-\frac {7}{11} \log (x+4) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.214, Rules used = {12, 616, 31} \[ \frac {7}{11} \log (3-2 x)-\frac {7}{11} \log (x+4) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 31
Rule 616
Rubi steps
\begin {align*} \int \frac {7}{-12+5 x+2 x^2} \, dx &=7 \int \frac {1}{-12+5 x+2 x^2} \, dx\\ &=\frac {14}{11} \int \frac {1}{-3+2 x} \, dx-\frac {14}{11} \int \frac {1}{8+2 x} \, dx\\ &=\frac {7}{11} \log (3-2 x)-\frac {7}{11} \log (4+x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 21, normalized size = 1.11 \[ 7 \left (\frac {1}{11} \log (3-2 x)-\frac {1}{11} \log (x+4)\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.39, size = 15, normalized size = 0.79 \[ \frac {7}{11} \, \log \left (2 \, x - 3\right ) - \frac {7}{11} \, \log \left (x + 4\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.08, size = 17, normalized size = 0.89 \[ \frac {7}{11} \, \log \left ({\left | 2 \, x - 3 \right |}\right ) - \frac {7}{11} \, \log \left ({\left | x + 4 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 16, normalized size = 0.84 \[ \frac {7 \ln \left (2 x -3\right )}{11}-\frac {7 \ln \left (x +4\right )}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.45, size = 15, normalized size = 0.79 \[ \frac {7}{11} \, \log \left (2 \, x - 3\right ) - \frac {7}{11} \, \log \left (x + 4\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.12, size = 8, normalized size = 0.42 \[ -\frac {14\,\mathrm {atanh}\left (\frac {4\,x}{11}+\frac {5}{11}\right )}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.11, size = 17, normalized size = 0.89 \[ \frac {7 \log {\left (x - \frac {3}{2} \right )}}{11} - \frac {7 \log {\left (x + 4 \right )}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________