Optimal. Leaf size=24 \[ -e^{9 x^2}+2 x+\frac {-x+x^4}{x} \]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 16, normalized size of antiderivative = 0.67, number of steps used = 2, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {2209} \begin {gather*} x^3-e^{9 x^2}+2 x \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 2209
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=2 x+x^3-18 \int e^{9 x^2} x \, dx\\ &=-e^{9 x^2}+2 x+x^3\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 16, normalized size = 0.67 \begin {gather*} -e^{9 x^2}+2 x+x^3 \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.67, size = 15, normalized size = 0.62 \begin {gather*} x^{3} + 2 \, x - e^{\left (9 \, x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.68, size = 15, normalized size = 0.62 \begin {gather*} x^{3} + 2 \, x - e^{\left (9 \, x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.02, size = 16, normalized size = 0.67
method | result | size |
default | \(x^{3}+2 x -{\mathrm e}^{9 x^{2}}\) | \(16\) |
norman | \(x^{3}+2 x -{\mathrm e}^{9 x^{2}}\) | \(16\) |
risch | \(x^{3}+2 x -{\mathrm e}^{9 x^{2}}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.49, size = 15, normalized size = 0.62 \begin {gather*} x^{3} + 2 \, x - e^{\left (9 \, x^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.05, size = 15, normalized size = 0.62 \begin {gather*} 2\,x-{\mathrm {e}}^{9\,x^2}+x^3 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.08, size = 12, normalized size = 0.50 \begin {gather*} x^{3} + 2 x - e^{9 x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________