3.1.81 \(\int \frac {F^{c+d x}}{(a+b F^{c+d x}) x^2} \, dx\) [81]

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

[Out]

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

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Rubi [A]
time = 0.05, 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 = {} \begin {gather*} \int \frac {F^{c+d x}}{\left (a+b F^{c+d x}\right ) x^2} \, dx \end {gather*}

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 = 0.24, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {F^{c+d x}}{\left (a+b F^{c+d x}\right ) x^2} \, dx \end {gather*}

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 = 0.01, size = 0, normalized size = 0.00 \[\int \frac {F^{d x +c}}{\left (a +b \,F^{d x +c}\right ) x^{2}}\, dx\]

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 = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

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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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

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

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 [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

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

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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