3.1.6 \(\int \frac {a+b \text {csch}(c+d x^2)}{x} \, dx\) [6]

Optimal. Leaf size=22 \[ a \log (x)+b \text {Int}\left (\frac {\text {csch}\left (c+d x^2\right )}{x},x\right ) \]

[Out]

a*ln(x)+b*Unintegrable(csch(d*x^2+c)/x,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 {a+b \text {csch}\left (c+d x^2\right )}{x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(a + b*Csch[c + d*x^2])/x,x]

[Out]

a*Log[x] + b*Defer[Int][Csch[c + d*x^2]/x, x]

Rubi steps

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

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Mathematica [A]
time = 6.05, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {a+b \text {csch}\left (c+d x^2\right )}{x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

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Maple [A]
time = 0.89, size = 0, normalized size = 0.00 \[\int \frac {a +b \,\mathrm {csch}\left (d \,x^{2}+c \right )}{x}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

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

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Mupad [A]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int \frac {a+\frac {b}{\mathrm {sinh}\left (d\,x^2+c\right )}}{x} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((a + b/sinh(c + d*x^2))/x,x)

[Out]

int((a + b/sinh(c + d*x^2))/x, x)

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