Optimal. Leaf size=22 \[ \text {Int}\left (\frac {e^{\frac {e}{(c+d x)^3}}}{a+b x},x\right ) \]
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Rubi [A] time = 0.02, 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 = {} \[ \int \frac {e^{\frac {e}{(c+d x)^3}}}{a+b x} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {e^{\frac {e}{(c+d x)^3}}}{a+b x} \, dx &=\int \frac {e^{\frac {e}{(c+d x)^3}}}{a+b x} \, dx\\ \end {align*}
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Mathematica [A] time = 0.03, size = 0, normalized size = 0.00 \[ \int \frac {e^{\frac {e}{(c+d x)^3}}}{a+b x} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.43, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {e^{\left (\frac {e}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right )}}{b x + a}, x\right ) \]
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 \[ \int \frac {e^{\left (\frac {e}{{\left (d x + c\right )}^{3}}\right )}}{b x + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.11, size = 0, normalized size = 0.00 \[ \int \frac {{\mathrm e}^{\frac {e}{\left (d x +c \right )^{3}}}}{b x +a}\, dx \]
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 \[ \int \frac {e^{\left (\frac {e}{{\left (d x + c\right )}^{3}}\right )}}{b x + a}\,{d x} \]
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 \[ \int \frac {{\mathrm {e}}^{\frac {e}{{\left (c+d\,x\right )}^3}}}{a+b\,x} \,d x \]
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 \[ \int \frac {e^{\frac {e}{c^{3} + 3 c^{2} d x + 3 c d^{2} x^{2} + d^{3} x^{3}}}}{a + b x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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