3.58 \(\int \frac {\cosh ((a+b x)^2)}{x^2} \, dx\)

Optimal. Leaf size=15 \[ \text {Int}\left (\frac {\cosh \left ((a+b x)^2\right )}{x^2},x\right ) \]

[Out]

Unintegrable(cosh((b*x+a)^2)/x^2,x)

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Rubi [A]  time = 0.04, 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 = {} \[ \int \frac {\cosh \left ((a+b x)^2\right )}{x^2} \, dx \]

Verification is Not applicable to the result.

[In]

Int[Cosh[(a + b*x)^2]/x^2,x]

[Out]

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

Rubi steps

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

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Mathematica [A]  time = 11.05, size = 0, normalized size = 0.00 \[ \int \frac {\cosh \left ((a+b x)^2\right )}{x^2} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[Cosh[(a + b*x)^2]/x^2,x]

[Out]

Integrate[Cosh[(a + b*x)^2]/x^2, x]

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fricas [A]  time = 0.66, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\cosh \left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}{x^{2}}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\cosh \left ({\left (b x + a\right )}^{2}\right )}{x^{2}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(cosh((b*x + a)^2)/x^2, x)

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maple [A]  time = 0.16, size = 0, normalized size = 0.00 \[ \int \frac {\cosh \left (\left (b x +a \right )^{2}\right )}{x^{2}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\cosh \left ({\left (b x + a\right )}^{2}\right )}{x^{2}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(cosh((b*x + a)^2)/x^2, x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.07 \[ \int \frac {\mathrm {cosh}\left ({\left (a+b\,x\right )}^2\right )}{x^2} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(cosh((a + b*x)^2)/x^2,x)

[Out]

int(cosh((a + b*x)^2)/x^2, x)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\cosh {\left (a^{2} + 2 a b x + b^{2} x^{2} \right )}}{x^{2}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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