Optimal. Leaf size=24 \[ \text {Int}\left (\sin ^2(e+f x) (a+b \csc (e+f x))^m,x\right ) \]
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Rubi [A] time = 0.04, 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 = {} \[ \int (a+b \csc (e+f x))^m \sin ^2(e+f x) \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int (a+b \csc (e+f x))^m \sin ^2(e+f x) \, dx &=\int (a+b \csc (e+f x))^m \sin ^2(e+f x) \, dx\\ \end {align*}
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Mathematica [A] time = 6.24, size = 0, normalized size = 0.00 \[ \int (a+b \csc (e+f x))^m \sin ^2(e+f x) \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.51, size = 0, normalized size = 0.00 \[ {\rm integral}\left (-{\left (\cos \left (f x + e\right )^{2} - 1\right )} {\left (b \csc \left (f x + e\right ) + a\right )}^{m}, x\right ) \]
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 \[ \int {\left (b \csc \left (f x + e\right ) + a\right )}^{m} \sin \left (f x + e\right )^{2}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 4.45, size = 0, normalized size = 0.00 \[ \int \left (a +b \csc \left (f x +e \right )\right )^{m} \left (\sin ^{2}\left (f x +e \right )\right )\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int {\left (b \csc \left (f x + e\right ) + a\right )}^{m} \sin \left (f x + e\right )^{2}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.04 \[ \int {\sin \left (e+f\,x\right )}^2\,{\left (a+\frac {b}{\sin \left (e+f\,x\right )}\right )}^m \,d x \]
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 \[ \int \left (a + b \csc {\left (e + f x \right )}\right )^{m} \sin ^{2}{\left (e + f x \right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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