\(\int e^{c+d x^2} \text {erfi}(a+b x) \, dx\) [300]

Optimal result

Integrand size = 16, antiderivative size = 16 \[ \int e^{c+d x^2} \text {erfi}(a+b x) \, dx=\text {Int}\left (e^{c+d x^2} \text {erfi}(a+b x),x\right ) \]

[Out]

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

Rubi [N/A]

Not integrable

Time = 0.01 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int e^{c+d x^2} \text {erfi}(a+b x) \, dx=\int e^{c+d x^2} \text {erfi}(a+b x) \, dx \]

[In]

Int[E^(c + d*x^2)*Erfi[a + b*x],x]

[Out]

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

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

Mathematica [N/A]

Not integrable

Time = 0.03 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int e^{c+d x^2} \text {erfi}(a+b x) \, dx=\int e^{c+d x^2} \text {erfi}(a+b x) \, dx \]

[In]

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

[Out]

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

Maple [N/A] (verified)

Not integrable

Time = 0.06 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.94

\[\int {\mathrm e}^{d \,x^{2}+c} \operatorname {erfi}\left (b x +a \right )d x\]

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.25 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.06 \[ \int e^{c+d x^2} \text {erfi}(a+b x) \, dx=\int { \operatorname {erfi}\left (b x + a\right ) e^{\left (d x^{2} + c\right )} \,d x } \]

[In]

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

[Out]

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

Sympy [N/A]

Not integrable

Time = 4.27 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.06 \[ \int e^{c+d x^2} \text {erfi}(a+b x) \, dx=e^{c} \int e^{d x^{2}} \operatorname {erfi}{\left (a + b x \right )}\, dx \]

[In]

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

[Out]

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

Maxima [N/A]

Not integrable

Time = 0.26 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.06 \[ \int e^{c+d x^2} \text {erfi}(a+b x) \, dx=\int { \operatorname {erfi}\left (b x + a\right ) e^{\left (d x^{2} + c\right )} \,d x } \]

[In]

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

[Out]

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

Giac [N/A]

Not integrable

Time = 0.26 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.06 \[ \int e^{c+d x^2} \text {erfi}(a+b x) \, dx=\int { \operatorname {erfi}\left (b x + a\right ) e^{\left (d x^{2} + c\right )} \,d x } \]

[In]

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

[Out]

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

Mupad [N/A]

Not integrable

Time = 6.08 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.06 \[ \int e^{c+d x^2} \text {erfi}(a+b x) \, dx=\int \mathrm {erfi}\left (a+b\,x\right )\,{\mathrm {e}}^{d\,x^2+c} \,d x \]

[In]

int(erfi(a + b*x)*exp(c + d*x^2),x)

[Out]

int(erfi(a + b*x)*exp(c + d*x^2), x)