3.420 \(\int \frac {e^{\frac {e}{(c+d x)^3}}}{a+b x} \, dx\)

Optimal. Leaf size=22 \[ \text {Int}\left (\frac {e^{\frac {e}{(c+d x)^3}}}{a+b x},x\right ) \]

[Out]

Unintegrable(exp(e/(d*x+c)^3)/(b*x+a),x)

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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.

[In]

Int[E^(e/(c + d*x)^3)/(a + b*x),x]

[Out]

Defer[Int][E^(e/(c + d*x)^3)/(a + b*x), x]

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.

[In]

Integrate[E^(e/(c + d*x)^3)/(a + b*x),x]

[Out]

Integrate[E^(e/(c + d*x)^3)/(a + b*x), x]

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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.

[In]

integrate(exp(e/(d*x+c)^3)/(b*x+a),x, algorithm="fricas")

[Out]

integral(e^(e/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3))/(b*x + a), x)

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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.

[In]

integrate(exp(e/(d*x+c)^3)/(b*x+a),x, algorithm="giac")

[Out]

integrate(e^(e/(d*x + c)^3)/(b*x + a), x)

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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.

[In]

int(exp(1/(d*x+c)^3*e)/(b*x+a),x)

[Out]

int(exp(1/(d*x+c)^3*e)/(b*x+a),x)

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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.

[In]

integrate(exp(e/(d*x+c)^3)/(b*x+a),x, algorithm="maxima")

[Out]

integrate(e^(e/(d*x + c)^3)/(b*x + a), x)

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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.

[In]

int(exp(e/(c + d*x)^3)/(a + b*x),x)

[Out]

int(exp(e/(c + d*x)^3)/(a + b*x), x)

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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.

[In]

integrate(exp(e/(d*x+c)**3)/(b*x+a),x)

[Out]

Integral(exp(e/(c**3 + 3*c**2*d*x + 3*c*d**2*x**2 + d**3*x**3))/(a + b*x), x)

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