Optimal. Leaf size=22 \[ \frac {-2+e^{\frac {\left (3+x^2\right )^2}{x^3}}+x}{1+x} \]
________________________________________________________________________________________
Rubi [F] time = 1.16, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {3 x^4+e^{\frac {9+6 x^2+x^4}{x^3}} \left (-27-27 x-6 x^2-6 x^3+x^5\right )}{x^4+2 x^5+x^6} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {3 x^4+e^{\frac {9+6 x^2+x^4}{x^3}} \left (-27-27 x-6 x^2-6 x^3+x^5\right )}{x^4 \left (1+2 x+x^2\right )} \, dx\\ &=\int \frac {3 x^4+e^{\frac {9+6 x^2+x^4}{x^3}} \left (-27-27 x-6 x^2-6 x^3+x^5\right )}{x^4 (1+x)^2} \, dx\\ &=\int \left (\frac {3}{(1+x)^2}+\frac {e^{\frac {\left (3+x^2\right )^2}{x^3}} \left (-27-27 x-6 x^2-6 x^3+x^5\right )}{x^4 (1+x)^2}\right ) \, dx\\ &=-\frac {3}{1+x}+\int \frac {e^{\frac {\left (3+x^2\right )^2}{x^3}} \left (-27-27 x-6 x^2-6 x^3+x^5\right )}{x^4 (1+x)^2} \, dx\\ &=-\frac {3}{1+x}+\int \left (-\frac {27 e^{\frac {\left (3+x^2\right )^2}{x^3}}}{x^4}+\frac {27 e^{\frac {\left (3+x^2\right )^2}{x^3}}}{x^3}-\frac {33 e^{\frac {\left (3+x^2\right )^2}{x^3}}}{x^2}+\frac {33 e^{\frac {\left (3+x^2\right )^2}{x^3}}}{x}-\frac {e^{\frac {\left (3+x^2\right )^2}{x^3}}}{(1+x)^2}-\frac {32 e^{\frac {\left (3+x^2\right )^2}{x^3}}}{1+x}\right ) \, dx\\ &=-\frac {3}{1+x}-27 \int \frac {e^{\frac {\left (3+x^2\right )^2}{x^3}}}{x^4} \, dx+27 \int \frac {e^{\frac {\left (3+x^2\right )^2}{x^3}}}{x^3} \, dx-32 \int \frac {e^{\frac {\left (3+x^2\right )^2}{x^3}}}{1+x} \, dx-33 \int \frac {e^{\frac {\left (3+x^2\right )^2}{x^3}}}{x^2} \, dx+33 \int \frac {e^{\frac {\left (3+x^2\right )^2}{x^3}}}{x} \, dx-\int \frac {e^{\frac {\left (3+x^2\right )^2}{x^3}}}{(1+x)^2} \, dx\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.24, size = 21, normalized size = 0.95 \begin {gather*} \frac {-3+e^{\frac {\left (3+x^2\right )^2}{x^3}}}{1+x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.66, size = 23, normalized size = 1.05 \begin {gather*} \frac {e^{\left (\frac {x^{4} + 6 \, x^{2} + 9}{x^{3}}\right )} - 3}{x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.41, size = 23, normalized size = 1.05 \begin {gather*} \frac {e^{\left (\frac {x^{4} + 6 \, x^{2} + 9}{x^{3}}\right )} - 3}{x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.18, size = 27, normalized size = 1.23
method | result | size |
risch | \(-\frac {3}{x +1}+\frac {{\mathrm e}^{\frac {\left (x^{2}+3\right )^{2}}{x^{3}}}}{x +1}\) | \(27\) |
norman | \(\frac {-3 x^{3}+{\mathrm e}^{\frac {x^{4}+6 x^{2}+9}{x^{3}}} x^{3}}{x^{3} \left (x +1\right )}\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.58, size = 27, normalized size = 1.23 \begin {gather*} \frac {e^{\left (x + \frac {6}{x} + \frac {9}{x^{3}}\right )}}{x + 1} - \frac {3}{x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.96, size = 25, normalized size = 1.14 \begin {gather*} \frac {3\,x+{\mathrm {e}}^{6/x}\,{\mathrm {e}}^{\frac {9}{x^3}}\,{\mathrm {e}}^x}{x+1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.17, size = 22, normalized size = 1.00 \begin {gather*} \frac {e^{\frac {x^{4} + 6 x^{2} + 9}{x^{3}}}}{x + 1} - \frac {3}{x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________