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

Optimal. Leaf size=17 \[ \text {Int}\left (\text {erfi}(b x) e^{c+d x^2},x\right ) \]

[Out]

Unintegrable(exp(d*x^2+c)*erfi(b*x),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 = {} \[ \int e^{c+d x^2} \text {Erfi}(b x) \, dx \]

Verification is Not applicable to the result.

[In]

Int[E^(c + d*x^2)*Erfi[b*x],x]

[Out]

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

Rubi steps

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

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Mathematica [A]  time = 0.04, size = 0, normalized size = 0.00 \[ \int e^{c+d x^2} \text {erfi}(b x) \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[E^(c + d*x^2)*Erfi[b*x],x]

[Out]

Integrate[E^(c + d*x^2)*Erfi[b*x], x]

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fricas [A]  time = 0.52, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\operatorname {erfi}\left (b x\right ) e^{\left (d x^{2} + c\right )}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(erfi(b*x)*e^(d*x^2 + c), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(erfi(b*x)*e^(d*x^2 + c), x)

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maple [A]  time = 0.06, size = 0, normalized size = 0.00 \[ \int {\mathrm e}^{d \,x^{2}+c} \erfi \left (b x \right )\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(erfi(b*x)*e^(d*x^2 + c), x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.06 \[ \int {\mathrm {e}}^{d\,x^2+c}\,\mathrm {erfi}\left (b\,x\right ) \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(c + d*x^2)*erfi(b*x),x)

[Out]

int(exp(c + d*x^2)*erfi(b*x), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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