Optimal. Leaf size=33 \[ -\frac {13 x}{225}+\frac {x^2}{30}+\frac {8}{189} \log (2+3 x)-\frac {1}{875} \log (1+5 x) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 33, normalized size of antiderivative = 1.00, number of steps
used = 6, number of rules used = 4, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {1368, 715, 646,
31} \begin {gather*} \frac {x^2}{30}-\frac {13 x}{225}+\frac {8}{189} \log (3 x+2)-\frac {1}{875} \log (5 x+1) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 31
Rule 646
Rule 715
Rule 1368
Rubi steps
\begin {align*} \int \frac {x}{15+\frac {2}{x^2}+\frac {13}{x}} \, dx &=\int \frac {x^3}{2+13 x+15 x^2} \, dx\\ &=\int \left (-\frac {13}{225}+\frac {x}{15}+\frac {26+139 x}{225 \left (2+13 x+15 x^2\right )}\right ) \, dx\\ &=-\frac {13 x}{225}+\frac {x^2}{30}+\frac {1}{225} \int \frac {26+139 x}{2+13 x+15 x^2} \, dx\\ &=-\frac {13 x}{225}+\frac {x^2}{30}-\frac {3}{175} \int \frac {1}{3+15 x} \, dx+\frac {40}{63} \int \frac {1}{10+15 x} \, dx\\ &=-\frac {13 x}{225}+\frac {x^2}{30}+\frac {8}{189} \log (2+3 x)-\frac {1}{875} \log (1+5 x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 33, normalized size = 1.00 \begin {gather*} -\frac {13 x}{225}+\frac {x^2}{30}+\frac {8}{189} \log (2+3 x)-\frac {1}{875} \log (1+5 x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.02, size = 26, normalized size = 0.79
method | result | size |
default | \(-\frac {13 x}{225}+\frac {x^{2}}{30}+\frac {8 \ln \left (2+3 x \right )}{189}-\frac {\ln \left (1+5 x \right )}{875}\) | \(26\) |
norman | \(-\frac {13 x}{225}+\frac {x^{2}}{30}+\frac {8 \ln \left (2+3 x \right )}{189}-\frac {\ln \left (1+5 x \right )}{875}\) | \(26\) |
risch | \(-\frac {13 x}{225}+\frac {x^{2}}{30}+\frac {8 \ln \left (2+3 x \right )}{189}-\frac {\ln \left (1+5 x \right )}{875}\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.31, size = 25, normalized size = 0.76 \begin {gather*} \frac {1}{30} \, x^{2} - \frac {13}{225} \, x - \frac {1}{875} \, \log \left (5 \, x + 1\right ) + \frac {8}{189} \, \log \left (3 \, x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.36, size = 25, normalized size = 0.76 \begin {gather*} \frac {1}{30} \, x^{2} - \frac {13}{225} \, x - \frac {1}{875} \, \log \left (5 \, x + 1\right ) + \frac {8}{189} \, \log \left (3 \, x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.04, size = 27, normalized size = 0.82 \begin {gather*} \frac {x^{2}}{30} - \frac {13 x}{225} - \frac {\log {\left (x + \frac {1}{5} \right )}}{875} + \frac {8 \log {\left (x + \frac {2}{3} \right )}}{189} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 4.19, size = 27, normalized size = 0.82 \begin {gather*} \frac {1}{30} \, x^{2} - \frac {13}{225} \, x - \frac {1}{875} \, \log \left ({\left | 5 \, x + 1 \right |}\right ) + \frac {8}{189} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 1.31, size = 21, normalized size = 0.64 \begin {gather*} \frac {8\,\ln \left (x+\frac {2}{3}\right )}{189}-\frac {13\,x}{225}-\frac {\ln \left (x+\frac {1}{5}\right )}{875}+\frac {x^2}{30} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________