3.1.30 \(\int \frac {\text {sech}(a+b x)}{(c+d x)^2} \, dx\) [30]

Optimal. Leaf size=17 \[ \text {Int}\left (\frac {\text {sech}(a+b x)}{(c+d x)^2},x\right ) \]

[Out]

Unintegrable(sech(b*x+a)/(d*x+c)^2,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 {sech}(a+b x)}{(c+d x)^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[Sech[a + b*x]/(c + d*x)^2,x]

[Out]

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

Rubi steps

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

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Mathematica [A]
time = 6.20, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\text {sech}(a+b x)}{(c+d x)^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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Maple [A]
time = 180.00, size = 0, normalized size = 0.00 \[\int \frac {\mathrm {sech}\left (b x +a \right )}{\left (d x +c \right )^{2}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

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

[Out]

integral(sech(b*x + a)/(d^2*x^2 + 2*c*d*x + c^2), x)

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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\operatorname {sech}{\left (a + b x \right )}}{\left (c + d x\right )^{2}}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

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

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.06 \begin {gather*} \int \frac {1}{\mathrm {cosh}\left (a+b\,x\right )\,{\left (c+d\,x\right )}^2} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(cosh(a + b*x)*(c + d*x)^2),x)

[Out]

int(1/(cosh(a + b*x)*(c + d*x)^2), x)

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