Optimal. Leaf size=24 \[ \frac {2}{3}+2 x+\frac {1}{3} \left (x-45 \left (e^{5/3}+x\right )^2\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 18, normalized size of antiderivative = 0.75, number of steps used = 1, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {9} \begin {gather*} -\frac {1}{540} \left (-90 x-90 e^{5/3}+7\right )^2 \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 9
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {1}{540} \left (7-90 e^{5/3}-90 x\right )^2\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 19, normalized size = 0.79 \begin {gather*} \frac {7 x}{3}-30 e^{5/3} x-15 x^2 \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.47, size = 14, normalized size = 0.58 \begin {gather*} -15 \, x^{2} - 30 \, x e^{\frac {5}{3}} + \frac {7}{3} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.19, size = 14, normalized size = 0.58 \begin {gather*} -15 \, x^{2} - 30 \, x e^{\frac {5}{3}} + \frac {7}{3} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.02, size = 13, normalized size = 0.54
method | result | size |
gosper | \(-\frac {x \left (45 x +90 \,{\mathrm e}^{\frac {5}{3}}-7\right )}{3}\) | \(13\) |
default | \(-30 x \,{\mathrm e}^{\frac {5}{3}}-15 x^{2}+\frac {7 x}{3}\) | \(15\) |
norman | \(\left (-30 \,{\mathrm e}^{\frac {5}{3}}+\frac {7}{3}\right ) x -15 x^{2}\) | \(15\) |
risch | \(-30 x \,{\mathrm e}^{\frac {5}{3}}-15 x^{2}+\frac {7 x}{3}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.40, size = 14, normalized size = 0.58 \begin {gather*} -15 \, x^{2} - 30 \, x e^{\frac {5}{3}} + \frac {7}{3} \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.67, size = 15, normalized size = 0.62 \begin {gather*} -15\,x^2+\left (\frac {7}{3}-30\,{\mathrm {e}}^{5/3}\right )\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.05, size = 15, normalized size = 0.62 \begin {gather*} - 15 x^{2} + x \left (\frac {7}{3} - 30 e^{\frac {5}{3}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________