Optimal. Leaf size=19 \[ \frac {2 e^4}{9 \left (3+\frac {4}{e^5}\right )^2 x} \]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.103, Rules used = {6, 12, 30} \begin {gather*} \frac {2 e^{14}}{9 \left (4+3 e^5\right )^2 x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 6
Rule 12
Rule 30
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int -\frac {2 e^{14}}{81 e^{10} x^2+\left (144+216 e^5\right ) x^2} \, dx\\ &=\int -\frac {2 e^{14}}{\left (144+216 e^5+81 e^{10}\right ) x^2} \, dx\\ &=-\frac {\left (2 e^{14}\right ) \int \frac {1}{x^2} \, dx}{9 \left (4+3 e^5\right )^2}\\ &=\frac {2 e^{14}}{9 \left (4+3 e^5\right )^2 x}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 19, normalized size = 1.00 \begin {gather*} \frac {2 e^{14}}{9 \left (4+3 e^5\right )^2 x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.50, size = 20, normalized size = 1.05 \begin {gather*} \frac {2 \, e^{14}}{9 \, {\left (9 \, x e^{10} + 24 \, x e^{5} + 16 \, x\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.16, size = 19, normalized size = 1.00 \begin {gather*} \frac {2 \, e^{14}}{9 \, x {\left (9 \, e^{10} + 24 \, e^{5} + 16\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.38, size = 20, normalized size = 1.05
method | result | size |
norman | \(\frac {2 \,{\mathrm e}^{4} {\mathrm e}^{10}}{9 \left (3 \,{\mathrm e}^{5}+4\right )^{2} x}\) | \(20\) |
risch | \(\frac {2 \,{\mathrm e}^{14}}{9 x \left (9 \,{\mathrm e}^{10}+24 \,{\mathrm e}^{5}+16\right )}\) | \(20\) |
gosper | \(\frac {2 \,{\mathrm e}^{4} {\mathrm e}^{10}}{9 x \left (9 \,{\mathrm e}^{10}+24 \,{\mathrm e}^{5}+16\right )}\) | \(26\) |
default | \(\frac {2 \,{\mathrm e}^{4} {\mathrm e}^{10}}{9 x \left (9 \,{\mathrm e}^{10}+24 \,{\mathrm e}^{5}+16\right )}\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.38, size = 19, normalized size = 1.00 \begin {gather*} \frac {2 \, e^{14}}{9 \, x {\left (9 \, e^{10} + 24 \, e^{5} + 16\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.17, size = 15, normalized size = 0.79 \begin {gather*} \frac {2\,{\mathrm {e}}^{14}}{9\,x\,{\left (3\,{\mathrm {e}}^5+4\right )}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.07, size = 17, normalized size = 0.89 \begin {gather*} \frac {2 e^{14}}{x \left (144 + 216 e^{5} + 81 e^{10}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________