Optimal. Leaf size=23 \[ \text {Int}\left (\frac {1}{(c+d x)^2 (a \cos (e+f x)+a)},x\right ) \]
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Rubi [A] time = 0.06, 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 = {} \[ \int \frac {1}{(c+d x)^2 (a+a \cos (e+f x))} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {1}{(c+d x)^2 (a+a \cos (e+f x))} \, dx &=\int \frac {1}{(c+d x)^2 (a+a \cos (e+f x))} \, dx\\ \end {align*}
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Mathematica [A] time = 2.69, size = 0, normalized size = 0.00 \[ \int \frac {1}{(c+d x)^2 (a+a \cos (e+f x))} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.65, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + {\left (a d^{2} x^{2} + 2 \, a c d x + a c^{2}\right )} \cos \left (f x + e\right )}, x\right ) \]
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 \[ \int \frac {1}{{\left (d x + c\right )}^{2} {\left (a \cos \left (f x + e\right ) + a\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.23, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (d x +c \right )^{2} \left (a +a \cos \left (f x +e \right )\right )}\, dx \]
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 = -0.04 \[ \int \frac {1}{\left (a+a\,\cos \left (e+f\,x\right )\right )\,{\left (c+d\,x\right )}^2} \,d x \]
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 \[ \frac {\int \frac {1}{c^{2} \cos {\left (e + f x \right )} + c^{2} + 2 c d x \cos {\left (e + f x \right )} + 2 c d x + d^{2} x^{2} \cos {\left (e + f x \right )} + d^{2} x^{2}}\, dx}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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