Optimal. Leaf size=23 \[ \text {Int}\left ((c+d x)^m (a \sin (e+f x)+a)^n,x\right ) \]
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Rubi [A] time = 0.05, 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 = {} \[ \int (c+d x)^m (a+a \sin (e+f x))^n \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int (c+d x)^m (a+a \sin (e+f x))^n \, dx &=\int (c+d x)^m (a+a \sin (e+f x))^n \, dx\\ \end {align*}
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Mathematica [A] time = 1.28, size = 0, normalized size = 0.00 \[ \int (c+d x)^m (a+a \sin (e+f x))^n \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.66, size = 0, normalized size = 0.00 \[ {\rm integral}\left ({\left (d x + c\right )}^{m} {\left (a \sin \left (f x + e\right ) + a\right )}^{n}, x\right ) \]
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 \[ \int {\left (d x + c\right )}^{m} {\left (a \sin \left (f x + e\right ) + a\right )}^{n}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.38, size = 0, normalized size = 0.00 \[ \int \left (d x +c \right )^{m} \left (a +a \sin \left (f x +e \right )\right )^{n}\, dx \]
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 \[ \int {\left (d x + c\right )}^{m} {\left (a \sin \left (f x + e\right ) + a\right )}^{n}\,{d x} \]
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 \[ \int {\left (a+a\,\sin \left (e+f\,x\right )\right )}^n\,{\left (c+d\,x\right )}^m \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [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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