3.1.61 \(\int e^{c+d x^2} \text {Erf}(b x) \, dx\) [61]

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

[Out]

Unintegrable(exp(d*x^2+c)*erf(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 = {} \begin {gather*} \int e^{c+d x^2} \text {Erf}(b x) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[E^(c + d*x^2)*Erf[b*x],x]

[Out]

Defer[Int][E^(c + d*x^2)*Erf[b*x], x]

Rubi steps

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

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Mathematica [A]
time = 0.02, size = 0, normalized size = 0.00 \begin {gather*} \int e^{c+d x^2} \text {Erf}(b x) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[E^(c + d*x^2)*Erf[b*x],x]

[Out]

Integrate[E^(c + d*x^2)*Erf[b*x], x]

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

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

[Out]

integral(erf(b*x)*e^(d*x^2 + c), x)

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} e^{c} \int e^{d x^{2}} \operatorname {erf}{\left (b x \right )}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

integrate(erf(b*x)*e^(d*x^2 + c), x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.06 \begin {gather*} \int {\mathrm {e}}^{d\,x^2+c}\,\mathrm {erf}\left (b\,x\right ) \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(c + d*x^2)*erf(b*x),x)

[Out]

int(exp(c + d*x^2)*erf(b*x), x)

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