Optimal. Leaf size=25 \[ \text {Int}\left (\frac {1}{x \left (a+b \sin \left (c+d (f+g x)^n\right )\right )},x\right ) \]
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Rubi [A] time = 0.03, 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 = {} \[ \int \frac {1}{x \left (a+b \sin \left (c+d (f+g x)^n\right )\right )} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {1}{x \left (a+b \sin \left (c+d (f+g x)^n\right )\right )} \, dx &=\int \frac {1}{x \left (a+b \sin \left (c+d (f+g x)^n\right )\right )} \, dx\\ \end {align*}
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Mathematica [A] time = 0.73, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \left (a+b \sin \left (c+d (f+g x)^n\right )\right )} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.79, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{b x \sin \left ({\left (g x + f\right )}^{n} d + c\right ) + a x}, x\right ) \]
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 \[ \int \frac {1}{{\left (b \sin \left ({\left (g x + f\right )}^{n} d + c\right ) + a\right )} x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.16, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \left (a +b \sin \left (c +d \left (g x +f \right )^{n}\right )\right )}\, dx \]
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 \[ \int \frac {1}{{\left (b \sin \left ({\left (g x + f\right )}^{n} d + c\right ) + a\right )} x}\,{d x} \]
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 \[ \int \frac {1}{x\,\left (a+b\,\sin \left (c+d\,{\left (f+g\,x\right )}^n\right )\right )} \,d x \]
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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