3.1.6 \(\int \frac {1}{(a+b e^{c+d x}) x^2} \, dx\) [6]

Optimal. Leaf size=20 \[ \text {Int}\left (\frac {1}{\left (a+b e^{c+d x}\right ) x^2},x\right ) \]

[Out]

Unintegrable(1/(a+b*exp(d*x+c))/x^2,x)

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Rubi [A]
time = 0.03, 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 {1}{\left (a+b e^{c+d x}\right ) x^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[1/((a + b*E^(c + d*x))*x^2),x]

[Out]

Defer[Int][1/((a + b*E^(c + d*x))*x^2), x]

Rubi steps

\begin {align*} \int \frac {1}{\left (a+b e^{c+d x}\right ) x^2} \, dx &=\int \frac {1}{\left (a+b e^{c+d x}\right ) x^2} \, dx\\ \end {align*}

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Mathematica [A]
time = 0.20, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{\left (a+b e^{c+d x}\right ) x^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[1/((a + b*E^(c + d*x))*x^2),x]

[Out]

Integrate[1/((a + b*E^(c + d*x))*x^2), x]

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Maple [A]
time = 0.05, size = 0, normalized size = 0.00 \[\int \frac {1}{\left (a +b \,{\mathrm e}^{d x +c}\right ) x^{2}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(a+b*exp(d*x+c))/x^2,x)

[Out]

int(1/(a+b*exp(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(1/(a+b*exp(d*x+c))/x^2,x, algorithm="maxima")

[Out]

integrate(1/((b*e^(d*x + c) + a)*x^2), 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(1/(a+b*exp(d*x+c))/x^2,x, algorithm="fricas")

[Out]

integral(1/(b*x^2*e^(d*x + c) + a*x^2), x)

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{x^{2} \left (a + b e^{c} e^{d x}\right )}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(a+b*exp(d*x+c))/x**2,x)

[Out]

Integral(1/(x**2*(a + b*exp(c)*exp(d*x))), 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(1/(a+b*exp(d*x+c))/x^2,x, algorithm="giac")

[Out]

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

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {1}{x^2\,\left (a+b\,{\mathrm {e}}^{c+d\,x}\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(x^2*(a + b*exp(c + d*x))),x)

[Out]

int(1/(x^2*(a + b*exp(c + d*x))), x)

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