3.73 \(\int \frac{(c+d x)^m}{a+b \left (F^{g (e+f x)}\right )^n} \, dx\)

Optimal. Leaf size=29 \[ \text{Int}\left (\frac{(c+d x)^m}{a+b \left (F^{e g+f g x}\right )^n},x\right ) \]

[Out]

Unintegrable[(c + d*x)^m/(a + b*(F^(e*g + f*g*x))^n), x]

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Rubi [A]  time = 0.180652, 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. \[ \text{Int}\left (\frac{(c+d x)^m}{a+b \left (F^{g (e+f x)}\right )^n},x\right ) \]

Verification is Not applicable to the result.

[In]  Int[(c + d*x)^m/(a + b*(F^(g*(e + f*x)))^n),x]

[Out]

Defer[Int][(c + d*x)^m/(a + b*(F^(e*g + f*g*x))^n), x]

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Rubi in Sympy [A]  time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (c + d x\right )^{m}}{a + b \left (F^{e g + f g x}\right )^{n}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((d*x+c)**m/(a+b*(F**(g*(f*x+e)))**n),x)

[Out]

Integral((c + d*x)**m/(a + b*(F**(e*g + f*g*x))**n), x)

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Mathematica [A]  time = 0.10983, size = 0, normalized size = 0. \[ \int \frac{(c+d x)^m}{a+b \left (F^{g (e+f x)}\right )^n} \, dx \]

Verification is Not applicable to the result.

[In]  Integrate[(c + d*x)^m/(a + b*(F^(g*(e + f*x)))^n),x]

[Out]

Integrate[(c + d*x)^m/(a + b*(F^(g*(e + f*x)))^n), x]

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Maple [A]  time = 0.08, size = 0, normalized size = 0. \[ \int{\frac{ \left ( dx+c \right ) ^{m}}{a+b \left ({F}^{g \left ( fx+e \right ) } \right ) ^{n}}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((d*x+c)^m/(a+b*(F^(g*(f*x+e)))^n),x)

[Out]

int((d*x+c)^m/(a+b*(F^(g*(f*x+e)))^n),x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (d x + c\right )}^{m}}{{\left (F^{{\left (f x + e\right )} g}\right )}^{n} b + a}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((d*x + c)^m/((F^((f*x + e)*g))^n*b + a),x, algorithm="maxima")

[Out]

integrate((d*x + c)^m/((F^((f*x + e)*g))^n*b + a), x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{{\left (d x + c\right )}^{m}}{{\left (F^{f g x + e g}\right )}^{n} b + a}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((d*x + c)^m/((F^((f*x + e)*g))^n*b + a),x, algorithm="fricas")

[Out]

integral((d*x + c)^m/((F^(f*g*x + e*g))^n*b + a), x)

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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((d*x+c)**m/(a+b*(F**(g*(f*x+e)))**n),x)

[Out]

Timed out

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GIAC/XCAS [A]  time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (d x + c\right )}^{m}}{{\left (F^{{\left (f x + e\right )} g}\right )}^{n} b + a}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((d*x + c)^m/((F^((f*x + e)*g))^n*b + a),x, algorithm="giac")

[Out]

integrate((d*x + c)^m/((F^((f*x + e)*g))^n*b + a), x)