Optimal. Leaf size=24 \[ \text{Unintegrable}\left (\frac{\left (a+b \sin \left (c+d (f+g x)^n\right )\right )^2}{x^2},x\right ) \]
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Rubi [A] time = 0.0255086, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{\left (a+b \sin \left (c+d (f+g x)^n\right )\right )^2}{x^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\left (a+b \sin \left (c+d (f+g x)^n\right )\right )^2}{x^2} \, dx &=\int \frac{\left (a+b \sin \left (c+d (f+g x)^n\right )\right )^2}{x^2} \, dx\\ \end{align*}
Mathematica [A] time = 3.16726, size = 0, normalized size = 0. \[ \int \frac{\left (a+b \sin \left (c+d (f+g x)^n\right )\right )^2}{x^2} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.293, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( a+b\sin \left ( c+d \left ( gx+f \right ) ^{n} \right ) \right ) ^{2}}{{x}^{2}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} -\frac{a^{2}}{x} - \frac{b^{2} x \int \frac{\cos \left (2 \,{\left (g x + f\right )}^{n} d + 2 \, c\right )}{x^{2}}\,{d x} - 4 \, a b x \int \frac{\sin \left ({\left (g x + f\right )}^{n} d + c\right )}{x^{2}}\,{d x} + b^{2}}{2 \, x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (-\frac{b^{2} \cos \left ({\left (g x + f\right )}^{n} d + c\right )^{2} - 2 \, a b \sin \left ({\left (g x + f\right )}^{n} d + c\right ) - a^{2} - b^{2}}{x^{2}}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\left (b \sin \left ({\left (g x + f\right )}^{n} d + c\right ) + a\right )}^{2}}{x^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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