Optimal. Leaf size=19 \[ \text {Int}\left (\frac {\text {erf}(a+b x)^2}{(c+d x)^2},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.02, 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 = {} \[ \int \frac {\text {Erf}(a+b x)^2}{(c+d x)^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int \frac {\text {erf}(a+b x)^2}{(c+d x)^2} \, dx &=\int \frac {\text {erf}(a+b x)^2}{(c+d x)^2} \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.12, size = 0, normalized size = 0.00 \[ \int \frac {\text {erf}(a+b x)^2}{(c+d x)^2} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.52, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\operatorname {erf}\left (b x + a\right )^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\operatorname {erf}\left (b x + a\right )^{2}}{{\left (d x + c\right )}^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.09, size = 0, normalized size = 0.00 \[ \int \frac {\erf \left (b x +a \right )^{2}}{\left (d x +c \right )^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ 4 \, b \int \frac {\operatorname {erf}\left (b x + a\right ) e^{\left (-b^{2} x^{2} - 2 \, a b x\right )}}{\sqrt {\pi } d^{2} x e^{\left (a^{2}\right )} + \sqrt {\pi } c d e^{\left (a^{2}\right )}}\,{d x} - \frac {\operatorname {erf}\left (b x + a\right )^{2}}{d^{2} x + c d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [A] time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {{\mathrm {erf}\left (a+b\,x\right )}^2}{{\left (c+d\,x\right )}^2} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\operatorname {erf}^{2}{\left (a + b x \right )}}{\left (c + d x\right )^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________