Optimal. Leaf size=27 \[ \frac {99}{x+3}+\frac {181}{x+4}+264 \log (x+3)-263 \log (x+4) \]
________________________________________________________________________________________
Rubi [A] time = 0.04, antiderivative size = 27, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.042, Rules used = {1620} \[ \frac {99}{x+3}+\frac {181}{x+4}+264 \log (x+3)-263 \log (x+4) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 1620
Rubi steps
\begin {align*} \int \frac {-9+3 x-6 x^2+x^3}{(3+x)^2 (4+x)^2} \, dx &=\int \left (-\frac {99}{(3+x)^2}+\frac {264}{3+x}-\frac {181}{(4+x)^2}-\frac {263}{4+x}\right ) \, dx\\ &=\frac {99}{3+x}+\frac {181}{4+x}+264 \log (3+x)-263 \log (4+x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.02, size = 27, normalized size = 1.00 \[ \frac {99}{x+3}+\frac {181}{x+4}+264 \log (x+3)-263 \log (x+4) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [A] time = 0.03, size = 29, normalized size = 1.07 \[ \frac {280 x+939}{(x+3) (x+4)}+264 \log (x+3)-263 \log (x+4) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.85, size = 45, normalized size = 1.67 \[ -\frac {263 \, {\left (x^{2} + 7 \, x + 12\right )} \log \left (x + 4\right ) - 264 \, {\left (x^{2} + 7 \, x + 12\right )} \log \left (x + 3\right ) - 280 \, x - 939}{x^{2} + 7 \, x + 12} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.86, size = 37, normalized size = 1.37 \[ \frac {181}{x + 4} - \frac {99}{\frac {1}{x + 4} - 1} + \log \left ({\left | x + 4 \right |}\right ) + 264 \, \log \left ({\left | -\frac {1}{x + 4} + 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.31, size = 28, normalized size = 1.04
method | result | size |
default | \(\frac {99}{3+x}+\frac {181}{4+x}+264 \ln \left (3+x \right )-263 \ln \left (4+x \right )\) | \(28\) |
norman | \(\frac {280 x +939}{\left (4+x \right ) \left (3+x \right )}+264 \ln \left (3+x \right )-263 \ln \left (4+x \right )\) | \(30\) |
risch | \(\frac {280 x +939}{\left (4+x \right ) \left (3+x \right )}+264 \ln \left (3+x \right )-263 \ln \left (4+x \right )\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.43, size = 29, normalized size = 1.07 \[ \frac {280 \, x + 939}{x^{2} + 7 \, x + 12} - 263 \, \log \left (x + 4\right ) + 264 \, \log \left (x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.19, size = 29, normalized size = 1.07 \[ 264\,\ln \left (x+3\right )-263\,\ln \left (x+4\right )+\frac {280\,x+939}{x^2+7\,x+12} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.15, size = 26, normalized size = 0.96 \[ \frac {280 x + 939}{x^{2} + 7 x + 12} + 264 \log {\left (x + 3 \right )} - 263 \log {\left (x + 4 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________