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

Optimal. Leaf size=16 \[ \text {Int}\left (\frac {\cosh \left (x^2+x+\frac {1}{4}\right )}{x},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.01, 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 = {} \[ \int \frac {\cosh \left (\frac {1}{4}+x+x^2\right )}{x} \, dx \]

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*}

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Mathematica [A]  time = 7.63, size = 0, normalized size = 0.00 \[ \int \frac {\cosh \left (\frac {1}{4}+x+x^2\right )}{x} \, dx \]

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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fricas [A]  time = 0.44, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\cosh \left (x^{2} + x + \frac {1}{4}\right )}{x}, x\right ) \]

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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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\cosh \left (x^{2} + x + \frac {1}{4}\right )}{x}\,{d x} \]

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)

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maple [A]  time = 0.13, size = 0, normalized size = 0.00 \[ \int \frac {\cosh \left (\frac {1}{4}+x +x^{2}\right )}{x}\, dx \]

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 = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\cosh \left (x^{2} + x + \frac {1}{4}\right )}{x}\,{d x} \]

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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mupad [A]  time = 0.00, size = -1, normalized size = -0.06 \[ \int \frac {\mathrm {cosh}\left (x^2+x+\frac {1}{4}\right )}{x} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(cosh(x + x^2 + 1/4)/x,x)

[Out]

int(cosh(x + x^2 + 1/4)/x, x)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\cosh {\left (x^{2} + x + \frac {1}{4} \right )}}{x}\, dx \]

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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