Integrand size = 16, antiderivative size = 16 \[ \int e^{c+d x^2} \text {erf}(a+b x) \, dx=\text {Int}\left (e^{c+d x^2} \text {erf}(a+b x),x\right ) \]
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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 = {} \[ \int e^{c+d x^2} \text {erf}(a+b x) \, dx=\int e^{c+d x^2} \text {erf}(a+b x) \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int e^{c+d x^2} \text {erf}(a+b x) \, dx \\ \end{align*}
Not integrable
Time = 0.03 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int e^{c+d x^2} \text {erf}(a+b x) \, dx=\int e^{c+d x^2} \text {erf}(a+b x) \, dx \]
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Not integrable
Time = 0.08 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.94
\[\int {\mathrm e}^{d \,x^{2}+c} \operatorname {erf}\left (b x +a \right )d x\]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.06 \[ \int e^{c+d x^2} \text {erf}(a+b x) \, dx=\int { \operatorname {erf}\left (b x + a\right ) e^{\left (d x^{2} + c\right )} \,d x } \]
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Not integrable
Time = 4.93 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.06 \[ \int e^{c+d x^2} \text {erf}(a+b x) \, dx=e^{c} \int e^{d x^{2}} \operatorname {erf}{\left (a + b x \right )}\, dx \]
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Not integrable
Time = 0.26 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.06 \[ \int e^{c+d x^2} \text {erf}(a+b x) \, dx=\int { \operatorname {erf}\left (b x + a\right ) e^{\left (d x^{2} + c\right )} \,d x } \]
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Not integrable
Time = 0.28 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.06 \[ \int e^{c+d x^2} \text {erf}(a+b x) \, dx=\int { \operatorname {erf}\left (b x + a\right ) e^{\left (d x^{2} + c\right )} \,d x } \]
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Not integrable
Time = 6.14 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.06 \[ \int e^{c+d x^2} \text {erf}(a+b x) \, dx=\int \mathrm {erf}\left (a+b\,x\right )\,{\mathrm {e}}^{d\,x^2+c} \,d x \]
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