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

Optimal. Leaf size=28 \[ \text{Int}\left (\frac{e^{x (a d+b c)+a c+b d x^2}}{x},x\right ) \]

[Out]

Unintegrable[E^(a*c + (b*c + a*d)*x + b*d*x^2)/x, x]

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Rubi [A]  time = 0.200442, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0. \[ \text{Int}\left (\frac{e^{(a+b x) (c+d x)}}{x},x\right ) \]

Verification is Not applicable to the result.

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

[Out]

Defer[Int][E^(a*c + (b*c + a*d)*x + b*d*x^2)/x, x]

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Rubi in Sympy [A]  time = 0., size = 0, normalized size = 0. \[ \int \frac{e^{a c + b d x^{2} + x \left (a d + b c\right )}}{x}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(exp((b*x+a)*(d*x+c))/x,x)

[Out]

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

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Mathematica [A]  time = 0.682612, size = 0, normalized size = 0. \[ \int \frac{e^{(a+b x) (c+d x)}}{x} \, dx \]

Verification is Not applicable to the result.

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

[Out]

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

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Maple [A]  time = 0.023, size = 0, normalized size = 0. \[ \int{\frac{{{\rm e}^{ \left ( dx+c \right ) \left ( bx+a \right ) }}}{x}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(exp((d*x+c)*(b*x+a))/x,x)

[Out]

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

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Maxima [A]  time = 0., size = 0, normalized size = 0. \[ \int \frac{e^{\left ({\left (b x + a\right )}{\left (d x + c\right )}\right )}}{x}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(e^((b*x + a)*(d*x + c))/x,x, algorithm="maxima")

[Out]

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

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Fricas [A]  time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{e^{\left (b d x^{2} + a c +{\left (b c + a d\right )} x\right )}}{x}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(e^((b*x + a)*(d*x + c))/x,x, algorithm="fricas")

[Out]

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

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Sympy [A]  time = 0., size = 0, normalized size = 0. \[ e^{a c} \int \frac{e^{a d x} e^{b c x} e^{b d x^{2}}}{x}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(exp((b*x+a)*(d*x+c))/x,x)

[Out]

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

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GIAC/XCAS [A]  time = 0., size = 0, normalized size = 0. \[ \int \frac{e^{\left ({\left (b x + a\right )}{\left (d x + c\right )}\right )}}{x}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(e^((b*x + a)*(d*x + c))/x,x, algorithm="giac")

[Out]

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