\(\int \frac {\text {erfc}(a+b x)^2}{c+d x} \, dx\) [141]

Optimal result

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

[Out]

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

Rubi [N/A]

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

[In]

Int[Erfc[a + b*x]^2/(c + d*x),x]

[Out]

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

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

Mathematica [N/A]

Not integrable

Time = 0.45 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\text {erfc}(a+b x)^2}{c+d x} \, dx=\int \frac {\text {erfc}(a+b x)^2}{c+d x} \, dx \]

[In]

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

[Out]

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

Maple [N/A] (verified)

Not integrable

Time = 0.19 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00

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

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.25 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.75 \[ \int \frac {\text {erfc}(a+b x)^2}{c+d x} \, dx=\int { \frac {\operatorname {erfc}\left (b x + a\right )^{2}}{d x + c} \,d x } \]

[In]

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

[Out]

integral((erf(b*x + a)^2 - 2*erf(b*x + a) + 1)/(d*x + c), x)

Sympy [N/A]

Not integrable

Time = 2.55 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.88 \[ \int \frac {\text {erfc}(a+b x)^2}{c+d x} \, dx=\int \frac {\operatorname {erfc}^{2}{\left (a + b x \right )}}{c + d x}\, dx \]

[In]

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

[Out]

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

Maxima [N/A]

Not integrable

Time = 0.22 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\text {erfc}(a+b x)^2}{c+d x} \, dx=\int { \frac {\operatorname {erfc}\left (b x + a\right )^{2}}{d x + c} \,d x } \]

[In]

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

[Out]

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

Giac [N/A]

Not integrable

Time = 0.28 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\text {erfc}(a+b x)^2}{c+d x} \, dx=\int { \frac {\operatorname {erfc}\left (b x + a\right )^{2}}{d x + c} \,d x } \]

[In]

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

[Out]

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

Mupad [N/A]

Not integrable

Time = 4.80 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\text {erfc}(a+b x)^2}{c+d x} \, dx=\int \frac {{\mathrm {erfc}\left (a+b\,x\right )}^2}{c+d\,x} \,d x \]

[In]

int(erfc(a + b*x)^2/(c + d*x),x)

[Out]

int(erfc(a + b*x)^2/(c + d*x), x)