3.81 \(\int \frac{F^{c+d x}}{\left (a+b F^{c+d x}\right ) x^2} \, dx\)

Optimal. Leaf size=27 \[ \text{Int}\left (\frac{F^{c+d x}}{x^2 \left (a+b F^{c+d x}\right )},x\right ) \]

[Out]

Unintegrable[F^(c + d*x)/((a + b*F^(c + d*x))*x^2), x]

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Rubi [A]  time = 0.0999374, 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. \[ \text{Int}\left (\frac{F^{c+d x}}{\left (a+b F^{c+d x}\right ) x^2},x\right ) \]

Verification is Not applicable to the result.

[In]  Int[F^(c + d*x)/((a + b*F^(c + d*x))*x^2),x]

[Out]

Defer[Int][F^(c + d*x)/((a + b*F^(c + d*x))*x^2), x]

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Rubi in Sympy [A]  time = 0., size = 0, normalized size = 0. \[ \int \frac{F^{c + d x}}{x^{2} \left (F^{c + d x} b + a\right )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(F**(d*x+c)/(a+b*F**(d*x+c))/x**2,x)

[Out]

Integral(F**(c + d*x)/(x**2*(F**(c + d*x)*b + a)), x)

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Mathematica [A]  time = 0.0553324, size = 0, normalized size = 0. \[ \int \frac{F^{c+d x}}{\left (a+b F^{c+d x}\right ) x^2} \, dx \]

Verification is Not applicable to the result.

[In]  Integrate[F^(c + d*x)/((a + b*F^(c + d*x))*x^2),x]

[Out]

Integrate[F^(c + d*x)/((a + b*F^(c + d*x))*x^2), x]

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Maple [A]  time = 0.036, size = 0, normalized size = 0. \[ \int{\frac{{F}^{dx+c}}{ \left ( a+b{F}^{dx+c} \right ){x}^{2}}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(F^(d*x+c)/(a+b*F^(d*x+c))/x^2,x)

[Out]

int(F^(d*x+c)/(a+b*F^(d*x+c))/x^2,x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \[ -a \int \frac{1}{F^{d x} F^{c} b^{2} x^{2} + a b x^{2}}\,{d x} - \frac{1}{b x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(F^(d*x + c)/((F^(d*x + c)*b + a)*x^2),x, algorithm="maxima")

[Out]

-a*integrate(1/(F^(d*x)*F^c*b^2*x^2 + a*b*x^2), x) - 1/(b*x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{F^{d x + c}}{F^{d x + c} b x^{2} + a x^{2}}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(F^(d*x + c)/((F^(d*x + c)*b + a)*x^2),x, algorithm="fricas")

[Out]

integral(F^(d*x + c)/(F^(d*x + c)*b*x^2 + a*x^2), x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \[ \int \frac{F^{c + d x}}{x^{2} \left (F^{c} F^{d x} b + a\right )}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(F**(d*x+c)/(a+b*F**(d*x+c))/x**2,x)

[Out]

Integral(F**(c + d*x)/(x**2*(F**c*F**(d*x)*b + a)), x)

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GIAC/XCAS [A]  time = 0., size = 0, normalized size = 0. \[ \int \frac{F^{d x + c}}{{\left (F^{d x + c} b + a\right )} x^{2}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(F^(d*x + c)/((F^(d*x + c)*b + a)*x^2),x, algorithm="giac")

[Out]

integrate(F^(d*x + c)/((F^(d*x + c)*b + a)*x^2), x)