Optimal. Leaf size=8 \[ \frac{\tan ^3(x)}{3} \]
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Rubi [A] time = 0.014444, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111, Rules used = {30} \[ \frac{\tan ^3(x)}{3} \]
Antiderivative was successfully verified.
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Rule 30
Rubi steps
\begin{align*} \int \frac{1}{(\csc (x)-\sin (x))^2} \, dx &=\operatorname{Subst}\left (\int x^2 \, dx,x,\tan (x)\right )\\ &=\frac{\tan ^3(x)}{3}\\ \end{align*}
Mathematica [A] time = 0.0029058, size = 8, normalized size = 1. \[ \frac{\tan ^3(x)}{3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.036, size = 7, normalized size = 0.9 \begin{align*}{\frac{ \left ( \tan \left ( x \right ) \right ) ^{3}}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.0229, size = 8, normalized size = 1. \begin{align*} \frac{1}{3} \, \tan \left (x\right )^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.97841, size = 50, normalized size = 6.25 \begin{align*} -\frac{{\left (\cos \left (x\right )^{2} - 1\right )} \sin \left (x\right )}{3 \, \cos \left (x\right )^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{\left (- \sin{\left (x \right )} + \csc{\left (x \right )}\right )^{2}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13383, size = 8, normalized size = 1. \begin{align*} \frac{1}{3} \, \tan \left (x\right )^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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