Optimal. Leaf size=21 \[ -\frac {1}{7} \log (2+3 x)+\frac {1}{7} \log (1+5 x) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 2, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {630, 31}
\begin {gather*} \frac {1}{7} \log (5 x+1)-\frac {1}{7} \log (3 x+2) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 31
Rule 630
Rubi steps
\begin {align*} \int \frac {1}{2+13 x+15 x^2} \, dx &=\frac {15}{7} \int \frac {1}{3+15 x} \, dx-\frac {15}{7} \int \frac {1}{10+15 x} \, dx\\ &=-\frac {1}{7} \log (2+3 x)+\frac {1}{7} \log (1+5 x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 21, normalized size = 1.00 \begin {gather*} -\frac {1}{7} \log (2+3 x)+\frac {1}{7} \log (1+5 x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.64, size = 18, normalized size = 0.86
method | result | size |
default | \(-\frac {\ln \left (2+3 x \right )}{7}+\frac {\ln \left (5 x +1\right )}{7}\) | \(18\) |
norman | \(-\frac {\ln \left (2+3 x \right )}{7}+\frac {\ln \left (5 x +1\right )}{7}\) | \(18\) |
risch | \(-\frac {\ln \left (2+3 x \right )}{7}+\frac {\ln \left (5 x +1\right )}{7}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.27, size = 17, normalized size = 0.81 \begin {gather*} \frac {1}{7} \, \log \left (5 \, x + 1\right ) - \frac {1}{7} \, \log \left (3 \, x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 2.03, size = 17, normalized size = 0.81 \begin {gather*} \frac {1}{7} \, \log \left (5 \, x + 1\right ) - \frac {1}{7} \, \log \left (3 \, x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.03, size = 15, normalized size = 0.71 \begin {gather*} \frac {\log {\left (x + \frac {1}{5} \right )}}{7} - \frac {\log {\left (x + \frac {2}{3} \right )}}{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 1.73, size = 19, normalized size = 0.90 \begin {gather*} \frac {1}{7} \, \log \left ({\left | 5 \, x + 1 \right |}\right ) - \frac {1}{7} \, \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 = 0.09, size = 8, normalized size = 0.38 \begin {gather*} -\frac {2\,\mathrm {atanh}\left (\frac {30\,x}{7}+\frac {13}{7}\right )}{7} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________