3.92 \(\int \frac{\sinh ((a+b x)^2)}{x^2} \, dx\)

Optimal. Leaf size=14 \[ \text{Unintegrable}\left (\frac{\sinh \left ((a+b x)^2\right )}{x^2},x\right ) \]

[Out]

Unintegrable[Sinh[(a + b*x)^2]/x^2, x]

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Rubi [A]  time = 0.0385763, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{\sinh \left ((a+b x)^2\right )}{x^2} \, dx \]

Verification is Not applicable to the result.

[In]

Int[Sinh[(a + b*x)^2]/x^2,x]

[Out]

b*Defer[Subst][Defer[Int][Sinh[x^2]/(-a + x)^2, x], x, a + b*x]

Rubi steps

\begin{align*} \int \frac{\sinh \left ((a+b x)^2\right )}{x^2} \, dx &=b \operatorname{Subst}\left (\int \frac{\sinh \left (x^2\right )}{(-a+x)^2} \, dx,x,a+b x\right )\\ \end{align*}

Mathematica [A]  time = 13.156, size = 0, normalized size = 0. \[ \int \frac{\sinh \left ((a+b x)^2\right )}{x^2} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[Sinh[(a + b*x)^2]/x^2,x]

[Out]

Integrate[Sinh[(a + b*x)^2]/x^2, x]

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Maple [A]  time = 0.044, size = 0, normalized size = 0. \begin{align*} \int{\frac{\sinh \left ( \left ( bx+a \right ) ^{2} \right ) }{{x}^{2}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(sinh((b*x+a)^2)/x^2,x)

[Out]

int(sinh((b*x+a)^2)/x^2,x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\sinh \left ({\left (b x + a\right )}^{2}\right )}{x^{2}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(sinh((b*x + a)^2)/x^2, x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\sinh \left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}{x^{2}}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integral(sinh(b^2*x^2 + 2*a*b*x + a^2)/x^2, x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\sinh{\left (a^{2} + 2 a b x + b^{2} x^{2} \right )}}{x^{2}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(sinh((b*x+a)**2)/x**2,x)

[Out]

Integral(sinh(a**2 + 2*a*b*x + b**2*x**2)/x**2, x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\sinh \left ({\left (b x + a\right )}^{2}\right )}{x^{2}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(sinh((b*x + a)^2)/x^2, x)