Optimal. Leaf size=34 \[ \frac {1-(3+x) \left (4+\frac {2 e^x}{5}-\log (4)\right )}{-2 x+\frac {3+x}{2}} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.38, antiderivative size = 39, normalized size of antiderivative = 1.15, number of steps
used = 13, number of rules used = 8, integrand size = 33, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.242, Rules used = {27, 12, 6873,
6874, 2230, 2225, 2208, 2209} \begin {gather*} \frac {4 e^x}{15}-\frac {16 e^x}{15 (1-x)}-\frac {2 (15-\log (256))}{3 (1-x)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 27
Rule 2208
Rule 2209
Rule 2225
Rule 2230
Rule 6873
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-150+e^x \left (-28+8 x+4 x^2\right )+40 \log (4)}{15 (-1+x)^2} \, dx\\ &=\frac {1}{15} \int \frac {-150+e^x \left (-28+8 x+4 x^2\right )+40 \log (4)}{(-1+x)^2} \, dx\\ &=\frac {1}{15} \int \frac {e^x \left (-28+8 x+4 x^2\right )-150 \left (1-\frac {8 \log (2)}{15}\right )}{(1-x)^2} \, dx\\ &=\frac {1}{15} \int \frac {2 \left (-14 e^x+4 e^x x+2 e^x x^2-75 \left (1-\frac {8 \log (2)}{15}\right )\right )}{(1-x)^2} \, dx\\ &=\frac {2}{15} \int \frac {-14 e^x+4 e^x x+2 e^x x^2-75 \left (1-\frac {8 \log (2)}{15}\right )}{(1-x)^2} \, dx\\ &=\frac {2}{15} \int \left (\frac {2 e^x \left (-7+2 x+x^2\right )}{(-1+x)^2}+\frac {5 (-15+\log (256))}{(-1+x)^2}\right ) \, dx\\ &=-\frac {2 (15-\log (256))}{3 (1-x)}+\frac {4}{15} \int \frac {e^x \left (-7+2 x+x^2\right )}{(-1+x)^2} \, dx\\ &=-\frac {2 (15-\log (256))}{3 (1-x)}+\frac {4}{15} \int \left (e^x-\frac {4 e^x}{(-1+x)^2}+\frac {4 e^x}{-1+x}\right ) \, dx\\ &=-\frac {2 (15-\log (256))}{3 (1-x)}+\frac {4 \int e^x \, dx}{15}-\frac {16}{15} \int \frac {e^x}{(-1+x)^2} \, dx+\frac {16}{15} \int \frac {e^x}{-1+x} \, dx\\ &=\frac {4 e^x}{15}-\frac {16 e^x}{15 (1-x)}+\frac {16}{15} e \text {Ei}(-1+x)-\frac {2 (15-\log (256))}{3 (1-x)}-\frac {16}{15} \int \frac {e^x}{-1+x} \, dx\\ &=\frac {4 e^x}{15}-\frac {16 e^x}{15 (1-x)}-\frac {2 (15-\log (256))}{3 (1-x)}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.05, size = 23, normalized size = 0.68 \begin {gather*} \frac {150+4 e^x (3+x)-40 \log (4)}{15 (-1+x)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 2.95, size = 31, normalized size = 0.91
method | result | size |
norman | \(\frac {\frac {4 \,{\mathrm e}^{x} x}{15}+\frac {4 \,{\mathrm e}^{x}}{5}+10-\frac {16 \ln \left (2\right )}{3}}{x -1}\) | \(22\) |
risch | \(\frac {10}{x -1}-\frac {16 \ln \left (2\right )}{3 \left (x -1\right )}+\frac {4 \left (3+x \right ) {\mathrm e}^{x}}{15 \left (x -1\right )}\) | \(30\) |
default | \(\frac {10}{x -1}+\frac {16 \,{\mathrm e}^{x}}{15 \left (x -1\right )}-\frac {16 \ln \left (2\right )}{3 \left (x -1\right )}+\frac {4 \,{\mathrm e}^{x}}{15}\) | \(31\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.36, size = 20, normalized size = 0.59 \begin {gather*} \frac {2 \, {\left (2 \, {\left (x + 3\right )} e^{x} - 40 \, \log \left (2\right ) + 75\right )}}{15 \, {\left (x - 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.06, size = 24, normalized size = 0.71 \begin {gather*} \frac {\left (4 x + 12\right ) e^{x}}{15 x - 15} - \frac {-30 + 16 \log {\left (2 \right )}}{3 x - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.41, size = 22, normalized size = 0.65 \begin {gather*} \frac {2 \, {\left (2 \, x e^{x} + 6 \, e^{x} - 40 \, \log \left (2\right ) + 75\right )}}{15 \, {\left (x - 1\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.15, size = 27, normalized size = 0.79 \begin {gather*} \frac {12\,{\mathrm {e}}^x-x\,\left (80\,\ln \left (2\right )-150\right )+4\,x\,{\mathrm {e}}^x}{15\,x-15} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________