Optimal. Leaf size=22 \[ 8+5 \left (e^{e^x}+\frac {5}{x \left (-3+x^3\right )}\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.38, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps
used = 7, number of rules used = 6, integrand size = 48, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {1608, 28, 6874,
2320, 2225, 460} \begin {gather*} 5 e^{e^x}-\frac {25}{x \left (3-x^3\right )} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 28
Rule 460
Rule 1608
Rule 2225
Rule 2320
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {75-100 x^3+e^{e^x+x} \left (45 x^2-30 x^5+5 x^8\right )}{x^2 \left (9-6 x^3+x^6\right )} \, dx\\ &=\int \frac {75-100 x^3+e^{e^x+x} \left (45 x^2-30 x^5+5 x^8\right )}{x^2 \left (-3+x^3\right )^2} \, dx\\ &=\int \left (5 e^{e^x+x}-\frac {25 \left (-3+4 x^3\right )}{x^2 \left (-3+x^3\right )^2}\right ) \, dx\\ &=5 \int e^{e^x+x} \, dx-25 \int \frac {-3+4 x^3}{x^2 \left (-3+x^3\right )^2} \, dx\\ &=-\frac {25}{x \left (3-x^3\right )}+5 \text {Subst}\left (\int e^x \, dx,x,e^x\right )\\ &=5 e^{e^x}-\frac {25}{x \left (3-x^3\right )}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.06, size = 20, normalized size = 0.91 \begin {gather*} 5 \left (e^{e^x}+\frac {5}{x \left (-3+x^3\right )}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.08, size = 19, normalized size = 0.86
method | result | size |
risch | \(\frac {25}{x \left (x^{3}-3\right )}+5 \,{\mathrm e}^{{\mathrm e}^{x}}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.53, size = 36, normalized size = 1.64 \begin {gather*} \frac {100 \, x^{2}}{9 \, {\left (x^{3} - 3\right )}} - \frac {25 \, {\left (4 \, x^{3} - 9\right )}}{9 \, {\left (x^{4} - 3 \, x\right )}} + 5 \, e^{\left (e^{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.37, size = 33, normalized size = 1.50 \begin {gather*} \frac {5 \, {\left ({\left (x^{4} - 3 \, x\right )} e^{\left (x + e^{x}\right )} + 5 \, e^{x}\right )} e^{\left (-x\right )}}{x^{4} - 3 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.11, size = 14, normalized size = 0.64 \begin {gather*} 5 e^{e^{x}} + \frac {25}{x^{4} - 3 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.41, size = 38, normalized size = 1.73 \begin {gather*} \frac {5 \, {\left (x^{4} e^{\left (x + e^{x}\right )} - 3 \, x e^{\left (x + e^{x}\right )} + 5 \, e^{x}\right )}}{x^{4} e^{x} - 3 \, x e^{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.16, size = 18, normalized size = 0.82 \begin {gather*} 5\,{\mathrm {e}}^{{\mathrm {e}}^x}+\frac {25}{x\,\left (x^3-3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________