Optimal. Leaf size=15 \[ \frac {1}{2 \left (1-e^{2 x}\right )} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {2282, 261} \[ \frac {1}{2 \left (1-e^{2 x}\right )} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 261
Rule 2282
Rubi steps
\begin {align*} \int \frac {1}{\left (-e^{-x}+e^x\right )^2} \, dx &=\operatorname {Subst}\left (\int \frac {x}{\left (1-x^2\right )^2} \, dx,x,e^x\right )\\ &=\frac {1}{2 \left (1-e^{2 x}\right )}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.02, size = 11, normalized size = 0.73 \[ \frac {1}{2-2 e^{2 x}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.40, size = 10, normalized size = 0.67 \[ -\frac {1}{2 \, {\left (e^{\left (2 \, x\right )} - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.20, size = 10, normalized size = 0.67 \[ -\frac {1}{2 \, {\left (e^{\left (2 \, x\right )} - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.02, size = 11, normalized size = 0.73 \[ -\frac {1}{2 \left ({\mathrm e}^{2 x}-1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.00, size = 10, normalized size = 0.67 \[ \frac {1}{2 \, {\left (e^{\left (-2 \, x\right )} - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 3.40, size = 12, normalized size = 0.80 \[ -\frac {1}{2\,\left ({\mathrm {e}}^{2\,x}-1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.08, size = 10, normalized size = 0.67 \[ - \frac {1}{2 e^{2 x} - 2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________