Optimal. Leaf size=19 \[ \frac {6}{-4+e^3+\frac {11 x}{4}-x^2} \]
________________________________________________________________________________________
Rubi [A] time = 0.03, antiderivative size = 20, normalized size of antiderivative = 1.05, number of steps used = 3, number of rules used = 3, integrand size = 47, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.064, Rules used = {1680, 12, 261} \begin {gather*} -\frac {384}{64 \left (x-\frac {11}{8}\right )^2-64 e^3+135} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 261
Rule 1680
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\operatorname {Subst}\left (\int \frac {49152 x}{\left (135-64 e^3+64 x^2\right )^2} \, dx,x,-\frac {11}{8}+x\right )\\ &=49152 \operatorname {Subst}\left (\int \frac {x}{\left (135-64 e^3+64 x^2\right )^2} \, dx,x,-\frac {11}{8}+x\right )\\ &=-\frac {384}{135-64 e^3+(-11+8 x)^2}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 19, normalized size = 1.00 \begin {gather*} -\frac {24}{16-4 e^3-11 x+4 x^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.13, size = 18, normalized size = 0.95 \begin {gather*} -\frac {24}{4 \, x^{2} - 11 \, x - 4 \, e^{3} + 16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: NotImplementedError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.07, size = 17, normalized size = 0.89
method | result | size |
risch | \(\frac {6}{\frac {11 x}{4}-x^{2}-4+{\mathrm e}^{3}}\) | \(17\) |
gosper | \(\frac {24}{-4 x^{2}+4 \,{\mathrm e}^{3}+11 x -16}\) | \(19\) |
norman | \(\frac {24}{-4 x^{2}+4 \,{\mathrm e}^{3}+11 x -16}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.34, size = 18, normalized size = 0.95 \begin {gather*} -\frac {24}{4 \, x^{2} - 11 \, x - 4 \, e^{3} + 16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.17, size = 18, normalized size = 0.95 \begin {gather*} \frac {24}{-4\,x^2+11\,x+4\,{\mathrm {e}}^3-16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.27, size = 17, normalized size = 0.89 \begin {gather*} - \frac {24}{4 x^{2} - 11 x - 4 e^{3} + 16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________