3.2.22 \(\int \frac {\text {Erfc}(a+b x)}{c+d x} \, dx\) [122]

Optimal. Leaf size=17 \[ \text {Int}\left (\frac {\text {Erfc}(a+b x)}{c+d x},x\right ) \]

[Out]

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

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Rubi [A]
time = 0.01, 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 = {} \begin {gather*} \int \frac {\text {Erfc}(a+b x)}{c+d x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[Erfc[a + b*x]/(c + d*x),x]

[Out]

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

Rubi steps

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

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Mathematica [A]
time = 0.09, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\text {Erfc}(a+b x)}{c+d x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[Erfc[a + b*x]/(c + d*x),x]

[Out]

Integrate[Erfc[a + b*x]/(c + d*x), x]

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Maple [A]
time = 0.17, size = 0, normalized size = 0.00 \[\int \frac {\mathrm {erfc}\left (b x +a \right )}{d x +c}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(erfc(b*x + a)/(d*x + c), x)

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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\operatorname {erfc}{\left (a + b x \right )}}{c + d x}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(erfc(a + b*x)/(c + d*x), x)

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Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(erfc(b*x + a)/(d*x + c), x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.06 \begin {gather*} \int \frac {\mathrm {erfc}\left (a+b\,x\right )}{c+d\,x} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(erfc(a + b*x)/(c + d*x),x)

[Out]

int(erfc(a + b*x)/(c + d*x), x)

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