Optimal. Leaf size=20 \[ \text {Int}\left (\frac {1}{\left (a+b e^{c+d x}\right )^3 x},x\right ) \]
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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 )^3 x} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {1}{\left (a+b e^{c+d x}\right )^3 x} \, dx &=\int \frac {1}{\left (a+b e^{c+d x}\right )^3 x} \, dx\\ \end {align*}
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Mathematica [A]
time = 2.24, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{\left (a+b e^{c+d x}\right )^3 x} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.16, size = 0, normalized size = 0.00 \[\int \frac {1}{\left (a +b \,{\mathrm e}^{d x +c}\right )^{3} x}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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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.
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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.
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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \frac {3 a d x + a + \left (2 b d x + b\right ) e^{c + d x}}{2 a^{4} d^{2} x^{2} + 4 a^{3} b d^{2} x^{2} e^{c + d x} + 2 a^{2} b^{2} d^{2} x^{2} e^{2 c + 2 d x}} + \frac {\int \frac {3 d x}{a x^{3} + b x^{3} e^{c} e^{d x}}\, dx + \int \frac {2 d^{2} x^{2}}{a x^{3} + b x^{3} e^{c} e^{d x}}\, dx + \int \frac {2}{a x^{3} + b x^{3} e^{c} e^{d x}}\, dx}{2 a^{2} d^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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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.
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Mupad [A]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {1}{x\,{\left (a+b\,{\mathrm {e}}^{c+d\,x}\right )}^3} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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