3.296 \(\int \frac {e^{c+d x^2} \text {erfi}(a+b x)}{x} \, dx\)

Optimal. Leaf size=22 \[ \text {Int}\left (\frac {e^{c+d x^2} \text {erfi}(a+b x)}{x},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.04, 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 = {} \[ \int \frac {e^{c+d x^2} \text {Erfi}(a+b x)}{x} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

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Mathematica [A]  time = 0.20, size = 0, normalized size = 0.00 \[ \int \frac {e^{c+d x^2} \text {erfi}(a+b x)}{x} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 0.48, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\operatorname {erfi}\left (b x + a\right ) e^{\left (d x^{2} + c\right )}}{x}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(d*x^2+c)*erfi(b*x+a)/x,x, algorithm="fricas")

[Out]

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

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\operatorname {erfi}\left (b x + a\right ) e^{\left (d x^{2} + c\right )}}{x}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(d*x^2+c)*erfi(b*x+a)/x,x, algorithm="giac")

[Out]

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

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maple [A]  time = 0.04, size = 0, normalized size = 0.00 \[ \int \frac {{\mathrm e}^{d \,x^{2}+c} \erfi \left (b x +a \right )}{x}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\operatorname {erfi}\left (b x + a\right ) e^{\left (d x^{2} + c\right )}}{x}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(d*x^2+c)*erfi(b*x+a)/x,x, algorithm="maxima")

[Out]

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

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mupad [A]  time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {\mathrm {erfi}\left (a+b\,x\right )\,{\mathrm {e}}^{d\,x^2+c}}{x} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ e^{c} \int \frac {e^{d x^{2}} \operatorname {erfi}{\left (a + b x \right )}}{x}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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