Optimal. Leaf size=46 \[ \frac {1}{2+x}+\frac {1}{4 (3+x)^2}+\frac {5}{4 (3+x)}+\frac {1}{8} \log (1+x)+2 \log (2+x)-\frac {17}{8} \log (3+x) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 46, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {90}
\begin {gather*} \frac {1}{x+2}+\frac {5}{4 (x+3)}+\frac {1}{4 (x+3)^2}+\frac {1}{8} \log (x+1)+2 \log (x+2)-\frac {17}{8} \log (x+3) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 90
Rubi steps
\begin {align*} \int \frac {1}{(1+x) (2+x)^2 (3+x)^3} \, dx &=\int \left (\frac {1}{8 (1+x)}-\frac {1}{(2+x)^2}+\frac {2}{2+x}-\frac {1}{2 (3+x)^3}-\frac {5}{4 (3+x)^2}-\frac {17}{8 (3+x)}\right ) \, dx\\ &=\frac {1}{2+x}+\frac {1}{4 (3+x)^2}+\frac {5}{4 (3+x)}+\frac {1}{8} \log (1+x)+2 \log (2+x)-\frac {17}{8} \log (3+x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 44, normalized size = 0.96 \begin {gather*} \frac {1}{8} \left (\frac {8}{2+x}+\frac {2}{(3+x)^2}+\frac {10}{3+x}+\log (-1-x)+16 \log (2+x)-17 \log (3+x)\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.07, size = 39, normalized size = 0.85
method | result | size |
default | \(\frac {1}{2+x}+\frac {1}{4 \left (3+x \right )^{2}}+\frac {5}{4 \left (3+x \right )}+\frac {\ln \left (1+x \right )}{8}+2 \ln \left (2+x \right )-\frac {17 \ln \left (3+x \right )}{8}\) | \(39\) |
norman | \(\frac {\frac {9}{4} x^{2}+\frac {25}{2} x +17}{\left (2+x \right ) \left (3+x \right )^{2}}+\frac {\ln \left (1+x \right )}{8}+2 \ln \left (2+x \right )-\frac {17 \ln \left (3+x \right )}{8}\) | \(41\) |
risch | \(\frac {\frac {9}{4} x^{2}+\frac {25}{2} x +17}{\left (2+x \right ) \left (3+x \right )^{2}}+\frac {\ln \left (1+x \right )}{8}+2 \ln \left (2+x \right )-\frac {17 \ln \left (3+x \right )}{8}\) | \(41\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 1.20, size = 46, normalized size = 1.00 \begin {gather*} \frac {9 \, x^{2} + 50 \, x + 68}{4 \, {\left (x^{3} + 8 \, x^{2} + 21 \, x + 18\right )}} - \frac {17}{8} \, \log \left (x + 3\right ) + 2 \, \log \left (x + 2\right ) + \frac {1}{8} \, \log \left (x + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 83 vs.
\(2 (38) = 76\).
time = 0.92, size = 83, normalized size = 1.80 \begin {gather*} \frac {18 \, x^{2} - 17 \, {\left (x^{3} + 8 \, x^{2} + 21 \, x + 18\right )} \log \left (x + 3\right ) + 16 \, {\left (x^{3} + 8 \, x^{2} + 21 \, x + 18\right )} \log \left (x + 2\right ) + {\left (x^{3} + 8 \, x^{2} + 21 \, x + 18\right )} \log \left (x + 1\right ) + 100 \, x + 136}{8 \, {\left (x^{3} + 8 \, x^{2} + 21 \, x + 18\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.08, size = 46, normalized size = 1.00 \begin {gather*} \frac {9 x^{2} + 50 x + 68}{4 x^{3} + 32 x^{2} + 84 x + 72} + \frac {\log {\left (x + 1 \right )}}{8} + 2 \log {\left (x + 2 \right )} - \frac {17 \log {\left (x + 3 \right )}}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.45, size = 52, normalized size = 1.13 \begin {gather*} \frac {1}{x + 2} - \frac {\frac {7}{x + 2} + 6}{4 \, {\left (\frac {1}{x + 2} + 1\right )}^{2}} + \frac {1}{8} \, \log \left ({\left | -\frac {1}{x + 2} + 1 \right |}\right ) - \frac {17}{8} \, \log \left ({\left | -\frac {1}{x + 2} - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.09, size = 45, normalized size = 0.98 \begin {gather*} \frac {\ln \left (x+1\right )}{8}+2\,\ln \left (x+2\right )-\frac {17\,\ln \left (x+3\right )}{8}+\frac {\frac {9\,x^2}{4}+\frac {25\,x}{2}+17}{x^3+8\,x^2+21\,x+18} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________