Optimal. Leaf size=27 \[ 4+x-\frac {x \log (2+25 (3-x))}{2 x-5 x^2} \]
________________________________________________________________________________________
Rubi [A] time = 0.19, antiderivative size = 17, normalized size of antiderivative = 0.63, number of steps used = 14, number of rules used = 7, integrand size = 45, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.156, Rules used = {6742, 44, 77, 88, 2395, 36, 31} \begin {gather*} x-\frac {\log (77-25 x)}{2-5 x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 31
Rule 36
Rule 44
Rule 77
Rule 88
Rule 2395
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {358}{(-2+5 x)^2 (-77+25 x)}+\frac {1765 x}{(-2+5 x)^2 (-77+25 x)}-\frac {2425 x^2}{(-2+5 x)^2 (-77+25 x)}+\frac {625 x^3}{(-2+5 x)^2 (-77+25 x)}-\frac {5 \log (77-25 x)}{(-2+5 x)^2}\right ) \, dx\\ &=-\left (5 \int \frac {\log (77-25 x)}{(-2+5 x)^2} \, dx\right )-358 \int \frac {1}{(-2+5 x)^2 (-77+25 x)} \, dx+625 \int \frac {x^3}{(-2+5 x)^2 (-77+25 x)} \, dx+1765 \int \frac {x}{(-2+5 x)^2 (-77+25 x)} \, dx-2425 \int \frac {x^2}{(-2+5 x)^2 (-77+25 x)} \, dx\\ &=-\frac {\log (77-25 x)}{2-5 x}+25 \int \frac {1}{(77-25 x) (-2+5 x)} \, dx-358 \int \left (-\frac {1}{67 (-2+5 x)^2}-\frac {5}{4489 (-2+5 x)}+\frac {25}{4489 (-77+25 x)}\right ) \, dx+625 \int \left (\frac {1}{625}-\frac {8}{8375 (-2+5 x)^2}-\frac {844}{561125 (-2+5 x)}+\frac {456533}{2805625 (-77+25 x)}\right ) \, dx+1765 \int \left (-\frac {2}{335 (-2+5 x)^2}-\frac {77}{22445 (-2+5 x)}+\frac {77}{4489 (-77+25 x)}\right ) \, dx-2425 \int \left (-\frac {4}{1675 (-2+5 x)^2}-\frac {288}{112225 (-2+5 x)}+\frac {5929}{112225 (-77+25 x)}\right ) \, dx\\ &=x+\frac {5}{67} \log (77-25 x)-\frac {\log (77-25 x)}{2-5 x}-\frac {5}{67} \log (2-5 x)+\frac {25}{67} \int \frac {1}{-2+5 x} \, dx+\frac {125}{67} \int \frac {1}{77-25 x} \, dx\\ &=x-\frac {\log (77-25 x)}{2-5 x}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.07, size = 44, normalized size = 1.63 \begin {gather*} x+\frac {10}{67} \tanh ^{-1}\left (\frac {1}{67} (-87+50 x)\right )+\left (\frac {5}{67}+\frac {1}{-2+5 x}\right ) \log (77-25 x)-\frac {5}{67} \log (2-5 x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.54, size = 23, normalized size = 0.85 \begin {gather*} \frac {5 \, x^{2} - 2 \, x + \log \left (-25 \, x + 77\right )}{5 \, x - 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.15, size = 16, normalized size = 0.59 \begin {gather*} x + \frac {\log \left (-25 \, x + 77\right )}{5 \, x - 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.07, size = 17, normalized size = 0.63
method | result | size |
risch | \(\frac {\ln \left (-25 x +77\right )}{5 x -2}+x\) | \(17\) |
norman | \(\frac {-2 x +\ln \left (-25 x +77\right )+5 x^{2}}{5 x -2}\) | \(24\) |
derivativedivides | \(x -\frac {77}{25}+\frac {5 \ln \left (-25 x +77\right )}{67}-\frac {5 \ln \left (-25 x +77\right ) \left (-25 x +77\right )}{67 \left (-25 x +10\right )}\) | \(32\) |
default | \(x -\frac {77}{25}+\frac {5 \ln \left (-25 x +77\right )}{67}-\frac {5 \ln \left (-25 x +77\right ) \left (-25 x +77\right )}{67 \left (-25 x +10\right )}\) | \(32\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [B] time = 0.41, size = 50, normalized size = 1.85 \begin {gather*} \frac {112225 \, x^{2} + 5 \, {\left (1790 \, x + 3773\right )} \log \left (-25 \, x + 77\right ) - 44890 \, x + 23986}{22445 \, {\left (5 \, x - 2\right )}} - \frac {358}{335 \, {\left (5 \, x - 2\right )}} - \frac {358}{4489} \, \log \left (25 \, x - 77\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 4.35, size = 16, normalized size = 0.59 \begin {gather*} x+\frac {\ln \left (77-25\,x\right )}{5\,x-2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.13, size = 12, normalized size = 0.44 \begin {gather*} x + \frac {\log {\left (77 - 25 x \right )}}{5 x - 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________