3.1.65 \(\int \sqrt {c+d x} \text {csch}(a+b x) \, dx\) [65]

Optimal. Leaf size=19 \[ \text {Int}\left (\sqrt {c+d x} \text {csch}(a+b x),x\right ) \]

[Out]

Unintegrable(csch(b*x+a)*(d*x+c)^(1/2),x)

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Rubi [A]
time = 0.02, 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 \sqrt {c+d x} \text {csch}(a+b x) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[Sqrt[c + d*x]*Csch[a + b*x],x]

[Out]

Defer[Int][Sqrt[c + d*x]*Csch[a + b*x], x]

Rubi steps

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

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Mathematica [A]
time = 23.35, size = 0, normalized size = 0.00 \begin {gather*} \int \sqrt {c+d x} \text {csch}(a+b x) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[Sqrt[c + d*x]*Csch[a + b*x],x]

[Out]

Integrate[Sqrt[c + d*x]*Csch[a + b*x], x]

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(csch(b*x+a)*(d*x+c)^(1/2),x)

[Out]

int(csch(b*x+a)*(d*x+c)^(1/2),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(csch(b*x+a)*(d*x+c)^(1/2),x, algorithm="maxima")

[Out]

integrate(sqrt(d*x + c)*csch(b*x + a), 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(csch(b*x+a)*(d*x+c)^(1/2),x, algorithm="fricas")

[Out]

integral(sqrt(d*x + c)*csch(b*x + a), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(csch(b*x+a)*(d*x+c)**(1/2),x)

[Out]

Integral(sqrt(c + d*x)*csch(a + b*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(csch(b*x+a)*(d*x+c)^(1/2),x, algorithm="giac")

[Out]

integrate(sqrt(d*x + c)*csch(b*x + a), x)

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {\sqrt {c+d\,x}}{\mathrm {sinh}\left (a+b\,x\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((c + d*x)^(1/2)/sinh(a + b*x),x)

[Out]

int((c + d*x)^(1/2)/sinh(a + b*x), x)

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