3.5.42 \(\int \frac {e^{(a+b x) (c+d x)}}{x} \, dx\) [442]

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

[Out]

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

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Rubi [A]
time = 0.09, 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^{(a+b x) (c+d x)}}{x} \, dx \end {gather*}

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]

Rubi steps

\begin {align*} \int \frac {e^{(a+b x) (c+d x)}}{x} \, dx &=\int \frac {e^{a c+(b c+a d) x+b d x^2}}{x} \, dx\\ \end {align*}

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Mathematica [A]
time = 0.49, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {e^{(a+b x) (c+d x)}}{x} \, dx \end {gather*}

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 = 0.01, size = 0, normalized size = 0.00 \[\int \frac {{\mathrm e}^{\left (b x +a \right ) \left (d x +c \right )}}{x}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

int(exp((b*x+a)*(d*x+c))/x,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((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 = 0.00, 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((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 = 0.00, size = 0, normalized size = 0.00 \begin {gather*} e^{a c} \int \frac {e^{a d x} e^{b c x} e^{b d x^{2}}}{x}\, dx \end {gather*}

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 [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((b*x+a)*(d*x+c))/x,x, algorithm="giac")

[Out]

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

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {{\mathrm {e}}^{\left (a+b\,x\right )\,\left (c+d\,x\right )}}{x} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp((a + b*x)*(c + d*x))/x,x)

[Out]

int(exp((a + b*x)*(c + d*x))/x, x)

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