3.4.95 \(\int \frac {e^{e (c+d x)^3}}{a+b x} \, dx\) [395]

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

[Out]

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

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Rubi [A]
time = 0.01, 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 {e^{e (c+d x)^3}}{a+b x} \, dx \end {gather*}

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^{e (c+d x)^3}}{a+b x} \, dx &=\int \frac {e^{e (c+d x)^3}}{a+b x} \, dx\\ \end {align*}

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Mathematica [A]
time = 0.55, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {e^{e (c+d x)^3}}{a+b x} \, dx \end {gather*}

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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Maple [A]
time = 0.02, size = 0, normalized size = 0.00 \[\int \frac {{\mathrm e}^{e \left (d x +c \right )^{3}}}{b x +a}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

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

[Out]

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

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} e^{c^{3} e} \int \frac {e^{d^{3} e x^{3}} e^{3 c d^{2} e x^{2}} e^{3 c^{2} d e x}}{a + b x}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

exp(c**3*e)*Integral(exp(d**3*e*x**3)*exp(3*c*d**2*e*x**2)*exp(3*c**2*d*e*x)/(a + b*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(exp(e*(d*x+c)^3)/(b*x+a),x, algorithm="giac")

[Out]

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

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {{\mathrm {e}}^{e\,{\left (c+d\,x\right )}^3}}{a+b\,x} \,d x \end {gather*}

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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