Optimal. Leaf size=29 \[ \text{Int}\left (\frac{1}{(c+d x)^2 \left (a+b \left (F^{e g+f g x}\right )^n\right )},x\right ) \]
[Out]
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Rubi [A] time = 0.184788, 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. \[ \text{Int}\left (\frac{1}{\left (a+b \left (F^{g (e+f x)}\right )^n\right ) (c+d x)^2},x\right ) \]
Verification is Not applicable to the result.
[In] Int[1/((a + b*(F^(g*(e + f*x)))^n)*(c + d*x)^2),x]
[Out]
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Rubi in Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b*(F**(g*(f*x+e)))**n)/(d*x+c)**2,x)
[Out]
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Mathematica [A] time = 0.461133, size = 0, normalized size = 0. \[ \int \frac{1}{\left (a+b \left (F^{g (e+f x)}\right )^n\right ) (c+d x)^2} \, dx \]
Verification is Not applicable to the result.
[In] Integrate[1/((a + b*(F^(g*(e + f*x)))^n)*(c + d*x)^2),x]
[Out]
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Maple [A] time = 0.135, size = 0, normalized size = 0. \[ \int{\frac{1}{ \left ( a+b \left ({F}^{g \left ( fx+e \right ) } \right ) ^{n} \right ) \left ( dx+c \right ) ^{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b*(F^(g*(f*x+e)))^n)/(d*x+c)^2,x)
[Out]
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Maxima [A] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left ({\left (F^{{\left (f x + e\right )} g}\right )}^{n} b + a\right )}{\left (d x + c\right )}^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(((F^((f*x + e)*g))^n*b + a)*(d*x + c)^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{1}{a d^{2} x^{2} + 2 \, a c d x + a c^{2} +{\left (b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right )}{\left (F^{f g x + e g}\right )}^{n}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(((F^((f*x + e)*g))^n*b + a)*(d*x + c)^2),x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+b*(F**(g*(f*x+e)))**n)/(d*x+c)**2,x)
[Out]
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GIAC/XCAS [A] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left ({\left (F^{{\left (f x + e\right )} g}\right )}^{n} b + a\right )}{\left (d x + c\right )}^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(((F^((f*x + e)*g))^n*b + a)*(d*x + c)^2),x, algorithm="giac")
[Out]