\(\int \frac {e^{c+d x^2} \text {erf}(a+b x)}{x} \, dx\) [88]

Optimal result

Integrand size = 19, antiderivative size = 19 \[ \int \frac {e^{c+d x^2} \text {erf}(a+b x)}{x} \, dx=\text {Int}\left (\frac {e^{c+d x^2} \text {erf}(a+b x)}{x},x\right ) \]

[Out]

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

Rubi [N/A]

Not integrable

Time = 0.03 (sec) , antiderivative size = 19, 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 = {} \[ \int \frac {e^{c+d x^2} \text {erf}(a+b x)}{x} \, dx=\int \frac {e^{c+d x^2} \text {erf}(a+b x)}{x} \, dx \]

[In]

Int[(E^(c + d*x^2)*Erf[a + b*x])/x,x]

[Out]

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

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

Mathematica [N/A]

Not integrable

Time = 0.15 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.11 \[ \int \frac {e^{c+d x^2} \text {erf}(a+b x)}{x} \, dx=\int \frac {e^{c+d x^2} \text {erf}(a+b x)}{x} \, dx \]

[In]

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

[Out]

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

Maple [N/A] (verified)

Not integrable

Time = 0.06 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.95

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

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.25 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.05 \[ \int \frac {e^{c+d x^2} \text {erf}(a+b x)}{x} \, dx=\int { \frac {\operatorname {erf}\left (b x + a\right ) e^{\left (d x^{2} + c\right )}}{x} \,d x } \]

[In]

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

[Out]

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

Sympy [N/A]

Not integrable

Time = 6.24 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00 \[ \int \frac {e^{c+d x^2} \text {erf}(a+b x)}{x} \, dx=e^{c} \int \frac {e^{d x^{2}} \operatorname {erf}{\left (a + b x \right )}}{x}\, dx \]

[In]

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

[Out]

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

Maxima [N/A]

Not integrable

Time = 0.26 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.05 \[ \int \frac {e^{c+d x^2} \text {erf}(a+b x)}{x} \, dx=\int { \frac {\operatorname {erf}\left (b x + a\right ) e^{\left (d x^{2} + c\right )}}{x} \,d x } \]

[In]

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

[Out]

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

Giac [N/A]

Not integrable

Time = 0.28 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.05 \[ \int \frac {e^{c+d x^2} \text {erf}(a+b x)}{x} \, dx=\int { \frac {\operatorname {erf}\left (b x + a\right ) e^{\left (d x^{2} + c\right )}}{x} \,d x } \]

[In]

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

[Out]

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

Mupad [N/A]

Not integrable

Time = 5.53 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.05 \[ \int \frac {e^{c+d x^2} \text {erf}(a+b x)}{x} \, dx=\int \frac {\mathrm {erf}\left (a+b\,x\right )\,{\mathrm {e}}^{d\,x^2+c}}{x} \,d x \]

[In]

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

[Out]

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