Integrand size = 16, antiderivative size = 16 \[ \int \frac {\text {erfi}(a+b x)^2}{c+d x} \, dx=\text {Int}\left (\frac {\text {erfi}(a+b x)^2}{c+d x},x\right ) \]
[Out]
Not integrable
Time = 0.02 (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 = {} \[ \int \frac {\text {erfi}(a+b x)^2}{c+d x} \, dx=\int \frac {\text {erfi}(a+b x)^2}{c+d x} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {\text {erfi}(a+b x)^2}{c+d x} \, dx \\ \end{align*}
Not integrable
Time = 0.04 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\text {erfi}(a+b x)^2}{c+d x} \, dx=\int \frac {\text {erfi}(a+b x)^2}{c+d x} \, dx \]
[In]
[Out]
Not integrable
Time = 0.19 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00
\[\int \frac {\operatorname {erfi}\left (b x +a \right )^{2}}{d x +c}d x\]
[In]
[Out]
Not integrable
Time = 0.25 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\text {erfi}(a+b x)^2}{c+d x} \, dx=\int { \frac {\operatorname {erfi}\left (b x + a\right )^{2}}{d x + c} \,d x } \]
[In]
[Out]
Not integrable
Time = 2.31 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int \frac {\text {erfi}(a+b x)^2}{c+d x} \, dx=\int \frac {\operatorname {erfi}^{2}{\left (a + b x \right )}}{c + d x}\, dx \]
[In]
[Out]
Not integrable
Time = 0.21 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\text {erfi}(a+b x)^2}{c+d x} \, dx=\int { \frac {\operatorname {erfi}\left (b x + a\right )^{2}}{d x + c} \,d x } \]
[In]
[Out]
Not integrable
Time = 0.25 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\text {erfi}(a+b x)^2}{c+d x} \, dx=\int { \frac {\operatorname {erfi}\left (b x + a\right )^{2}}{d x + c} \,d x } \]
[In]
[Out]
Not integrable
Time = 4.87 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\text {erfi}(a+b x)^2}{c+d x} \, dx=\int \frac {{\mathrm {erfi}\left (a+b\,x\right )}^2}{c+d\,x} \,d x \]
[In]
[Out]