Optimal. Leaf size=30 \[ \log \left (\frac {2}{5 \left (3-x+\frac {4}{4-\frac {1}{20} (5-x) (3+x)}\right )}\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.05, antiderivative size = 28, normalized size of antiderivative = 0.93, number of steps
used = 4, number of rules used = 3, integrand size = 46, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.065, Rules used = {2099, 642,
1601} \begin {gather*} \log \left (x^2-2 x+65\right )-\log \left (-x^3+5 x^2-71 x+275\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 642
Rule 1601
Rule 2099
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {2 (-1+x)}{65-2 x+x^2}+\frac {-71+10 x-3 x^2}{-275+71 x-5 x^2+x^3}\right ) \, dx\\ &=2 \int \frac {-1+x}{65-2 x+x^2} \, dx+\int \frac {-71+10 x-3 x^2}{-275+71 x-5 x^2+x^3} \, dx\\ &=\log \left (65-2 x+x^2\right )-\log \left (275-71 x+5 x^2-x^3\right )\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 28, normalized size = 0.93 \begin {gather*} \log \left (65-2 x+x^2\right )-\log \left (275-71 x+5 x^2-x^3\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.03, size = 27, normalized size = 0.90
method | result | size |
default | \(-\ln \left (x^{3}-5 x^{2}+71 x -275\right )+\ln \left (x^{2}-2 x +65\right )\) | \(27\) |
norman | \(-\ln \left (x^{3}-5 x^{2}+71 x -275\right )+\ln \left (x^{2}-2 x +65\right )\) | \(27\) |
risch | \(-\ln \left (x^{3}-5 x^{2}+71 x -275\right )+\ln \left (x^{2}-2 x +65\right )\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.26, size = 26, normalized size = 0.87 \begin {gather*} -\log \left (x^{3} - 5 \, x^{2} + 71 \, x - 275\right ) + \log \left (x^{2} - 2 \, x + 65\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.32, size = 26, normalized size = 0.87 \begin {gather*} -\log \left (x^{3} - 5 \, x^{2} + 71 \, x - 275\right ) + \log \left (x^{2} - 2 \, x + 65\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.05, size = 24, normalized size = 0.80 \begin {gather*} \log {\left (x^{2} - 2 x + 65 \right )} - \log {\left (x^{3} - 5 x^{2} + 71 x - 275 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.40, size = 27, normalized size = 0.90 \begin {gather*} \log \left (x^{2} - 2 \, x + 65\right ) - \log \left ({\left | x^{3} - 5 \, x^{2} + 71 \, x - 275 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.56, size = 26, normalized size = 0.87 \begin {gather*} \ln \left (x^2-2\,x+65\right )-\ln \left (x^3-5\,x^2+71\,x-275\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________