### 3.14 $$\int \frac{\cosh (\frac{1}{4}+x+x^2)}{x} \, dx$$

Optimal. Leaf size=15 $\text{Unintegrable}\left (\frac{\cosh \left (x^2+x+\frac{1}{4}\right )}{x},x\right )$

[Out]

Unintegrable[Cosh[1/4 + x + x^2]/x, x]

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Rubi [A]  time = 0.0101773, 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 = {} $\int \frac{\cosh \left (\frac{1}{4}+x+x^2\right )}{x} \, dx$

Veriﬁcation is Not applicable to the result.

[In]

Int[Cosh[1/4 + x + x^2]/x,x]

[Out]

Defer[Int][Cosh[1/4 + x + x^2]/x, x]

Rubi steps

\begin{align*} \int \frac{\cosh \left (\frac{1}{4}+x+x^2\right )}{x} \, dx &=\int \frac{\cosh \left (\frac{1}{4}+x+x^2\right )}{x} \, dx\\ \end{align*}

Mathematica [A]  time = 7.30575, size = 0, normalized size = 0. $\int \frac{\cosh \left (\frac{1}{4}+x+x^2\right )}{x} \, dx$

Veriﬁcation is Not applicable to the result.

[In]

Integrate[Cosh[1/4 + x + x^2]/x,x]

[Out]

Integrate[Cosh[1/4 + x + x^2]/x, x]

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Maple [A]  time = 0.026, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{x}\cosh \left ({\frac{1}{4}}+x+{x}^{2} \right ) }\, dx \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(cosh(1/4+x+x^2)/x,x)

[Out]

int(cosh(1/4+x+x^2)/x,x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\cosh \left (x^{2} + x + \frac{1}{4}\right )}{x}\,{d x} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(cosh(1/4+x+x^2)/x,x, algorithm="maxima")

[Out]

integrate(cosh(x^2 + x + 1/4)/x, x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\cosh \left (x^{2} + x + \frac{1}{4}\right )}{x}, x\right ) \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(cosh(1/4+x+x^2)/x,x, algorithm="fricas")

[Out]

integral(cosh(x^2 + x + 1/4)/x, x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\cosh{\left (x^{2} + x + \frac{1}{4} \right )}}{x}\, dx \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(cosh(1/4+x+x**2)/x,x)

[Out]

Integral(cosh(x**2 + x + 1/4)/x, x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\cosh \left (x^{2} + x + \frac{1}{4}\right )}{x}\,{d x} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(cosh(1/4+x+x^2)/x,x, algorithm="giac")

[Out]

integrate(cosh(x^2 + x + 1/4)/x, x)