Optimal. Leaf size=8 \[ -\frac {1}{2} \csc ^2(x) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.286, Rules used = {2606, 30} \[ -\frac {1}{2} \csc ^2(x) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 30
Rule 2606
Rubi steps
\begin {align*} \int \cot (x) \csc ^2(x) \, dx &=-\operatorname {Subst}(\int x \, dx,x,\csc (x))\\ &=-\frac {1}{2} \csc ^2(x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 8, normalized size = 1.00 \[ -\frac {1}{2} \csc ^2(x) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.41, size = 10, normalized size = 1.25 \[ \frac {1}{2 \, {\left (\cos \relax (x)^{2} - 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.01, size = 6, normalized size = 0.75 \[ -\frac {1}{2 \, \sin \relax (x)^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.02, size = 7, normalized size = 0.88 \[ -\frac {1}{2 \sin \relax (x )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.49, size = 6, normalized size = 0.75 \[ -\frac {1}{2 \, \sin \relax (x)^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.42, size = 6, normalized size = 0.75 \[ -\frac {{\mathrm {cot}\relax (x)}^2}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.07, size = 8, normalized size = 1.00 \[ - \frac {1}{2 \sin ^{2}{\relax (x )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________