Optimal. Leaf size=24 \[ e^{\frac {13}{10 x}-(-1+x) x}+x-\log (-1+x) \]
________________________________________________________________________________________
Rubi [A] time = 0.74, antiderivative size = 26, normalized size of antiderivative = 1.08, number of steps used = 6, number of rules used = 4, integrand size = 67, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.060, Rules used = {1593, 6742, 43, 6706} \begin {gather*} e^{-x^2+x+\frac {13}{10 x}}+x-\log (1-x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rule 1593
Rule 6706
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-20 x^2+10 x^3+e^{\frac {13+10 x^2-10 x^3}{10 x}} \left (13-13 x-10 x^2+30 x^3-20 x^4\right )}{x^2 (-10+10 x)} \, dx\\ &=\int \left (\frac {-2+x}{-1+x}-\frac {e^{\frac {13}{10 x}+x-x^2} \left (13-10 x^2+20 x^3\right )}{10 x^2}\right ) \, dx\\ &=-\left (\frac {1}{10} \int \frac {e^{\frac {13}{10 x}+x-x^2} \left (13-10 x^2+20 x^3\right )}{x^2} \, dx\right )+\int \frac {-2+x}{-1+x} \, dx\\ &=e^{\frac {13}{10 x}+x-x^2}+\int \left (1+\frac {1}{1-x}\right ) \, dx\\ &=e^{\frac {13}{10 x}+x-x^2}+x-\log (1-x)\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.17, size = 34, normalized size = 1.42 \begin {gather*} \frac {1}{10} \left (10 e^{\frac {13}{10 x}+x-x^2}+10 x-10 \log (1-x)\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.56, size = 26, normalized size = 1.08 \begin {gather*} x + e^{\left (-\frac {10 \, x^{3} - 10 \, x^{2} - 13}{10 \, x}\right )} - \log \left (x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.21, size = 26, normalized size = 1.08 \begin {gather*} x + e^{\left (-\frac {10 \, x^{3} - 10 \, x^{2} - 13}{10 \, x}\right )} - \log \left (x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.29, size = 27, normalized size = 1.12
method | result | size |
risch | \(x -\ln \left (x -1\right )+{\mathrm e}^{-\frac {10 x^{3}-10 x^{2}-13}{10 x}}\) | \(27\) |
norman | \(\frac {x^{2}+x \,{\mathrm e}^{\frac {-10 x^{3}+10 x^{2}+13}{10 x}}}{x}-\ln \left (x -1\right )\) | \(36\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.44, size = 21, normalized size = 0.88 \begin {gather*} x + e^{\left (-x^{2} + x + \frac {13}{10 \, x}\right )} - \log \left (x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 4.05, size = 21, normalized size = 0.88 \begin {gather*} x-\ln \left (x-1\right )+{\mathrm {e}}^{x+\frac {13}{10\,x}-x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.18, size = 19, normalized size = 0.79 \begin {gather*} x + e^{\frac {- x^{3} + x^{2} + \frac {13}{10}}{x}} - \log {\left (x - 1 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________