Optimal. Leaf size=19 \[ \text {Int}\left ((d x)^m \left (a+b \csc ^{-1}(c x)\right )^2,x\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int (d x)^m \left (a+b \csc ^{-1}(c x)\right )^2 \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int (d x)^m \left (a+b \csc ^{-1}(c x)\right )^2 \, dx &=\int (d x)^m \left (a+b \csc ^{-1}(c x)\right )^2 \, dx\\ \end {align*}
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Mathematica [A] time = 4.86, size = 0, normalized size = 0.00 \[ \int (d x)^m \left (a+b \csc ^{-1}(c x)\right )^2 \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.46, size = 0, normalized size = 0.00 \[ {\rm integral}\left ({\left (b^{2} \operatorname {arccsc}\left (c x\right )^{2} + 2 \, a b \operatorname {arccsc}\left (c x\right ) + a^{2}\right )} \left (d x\right )^{m}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int {\left (b \operatorname {arccsc}\left (c x\right ) + a\right )}^{2} \left (d x\right )^{m}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 3.97, size = 0, normalized size = 0.00 \[ \int \left (d x \right )^{m} \left (a +b \,\mathrm {arccsc}\left (c x \right )\right )^{2}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.05 \[ \int {\left (d\,x\right )}^m\,{\left (a+b\,\mathrm {asin}\left (\frac {1}{c\,x}\right )\right )}^2 \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \left (d x\right )^{m} \left (a + b \operatorname {acsc}{\left (c x \right )}\right )^{2}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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