Optimal. Leaf size=20 \[ \text {Int}\left (\frac {1}{\left (a+b e^{c+d x}\right )^3 x^2},x\right ) \]
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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^2} \, 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^2} \, dx &=\int \frac {1}{\left (a+b e^{c+d x}\right )^3 x^2} \, dx\\ \end {align*}
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Mathematica [A]
time = 1.15, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{\left (a+b e^{c+d x}\right )^3 x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.17, size = 0, normalized size = 0.00 \[\int \frac {1}{\left (a +b \,{\mathrm e}^{d x +c}\right )^{3} x^{2}}\, dx\]
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 + 2 a + \left (2 b d x + 2 b\right ) e^{c + d x}}{2 a^{4} d^{2} x^{3} + 4 a^{3} b d^{2} x^{3} e^{c + d x} + 2 a^{2} b^{2} d^{2} x^{3} e^{2 c + 2 d x}} + \frac {\int \frac {3 d x}{a x^{4} + b x^{4} e^{c} e^{d x}}\, dx + \int \frac {d^{2} x^{2}}{a x^{4} + b x^{4} e^{c} e^{d x}}\, dx + \int \frac {3}{a x^{4} + b x^{4} e^{c} e^{d x}}\, dx}{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^2\,{\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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