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

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

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Rubi [A]  time = 0.07, 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 = {} \[ \int \frac {F^{c+d x}}{\left (a+b F^{c+d x}\right ) x^2} \, dx \]

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]

Rubi steps

\begin {align*} \int \frac {F^{c+d x}}{\left (a+b F^{c+d x}\right ) x^2} \, dx &=\int \frac {F^{c+d x}}{\left (a+b F^{c+d x}\right ) x^2} \, dx\\ \end {align*}

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Mathematica [A]  time = 0.07, size = 0, normalized size = 0.00 \[ \int \frac {F^{c+d x}}{\left (a+b F^{c+d x}\right ) x^2} \, dx \]

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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fricas [A]  time = 0.43, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {F^{d x + c}}{F^{d x + c} b x^{2} + a x^{2}}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F^(d*x+c)/(a+b*F^(d*x+c))/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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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {F^{d x + c}}{{\left (F^{d x + c} b + a\right )} x^{2}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maple [A]  time = 0.08, size = 0, normalized size = 0.00 \[ \int \frac {F^{d x +c}}{\left (b \,F^{d x +c}+a \right ) x^{2}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ -a \int \frac {1}{F^{d x} F^{c} b^{2} x^{2} + a b x^{2}}\,{d x} - \frac {1}{b x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(F^(d*x+c)/(a+b*F^(d*x+c))/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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mupad [A]  time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {F^{c+d\,x}}{x^2\,\left (a+F^{c+d\,x}\,b\right )} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {F^{c + d x}}{x^{2} \left (F^{c} F^{d x} b + a\right )}\, dx \]

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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