\(\int \frac {\cos (\frac {1}{4}+x+x^2)}{x} \, dx\) [14]

Optimal result

Integrand size = 13, antiderivative size = 13 \[ \int \frac {\cos \left (\frac {1}{4}+x+x^2\right )}{x} \, dx=\text {Int}\left (\frac {\cos \left (\frac {1}{4}+x+x^2\right )}{x},x\right ) \]

[Out]

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

Rubi [N/A]

Not integrable

Time = 0.01 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {\cos \left (\frac {1}{4}+x+x^2\right )}{x} \, dx=\int \frac {\cos \left (\frac {1}{4}+x+x^2\right )}{x} \, dx \]

[In]

Int[Cos[1/4 + x + x^2]/x,x]

[Out]

Defer[Int][Cos[1/4 + x + x^2]/x, x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {\cos \left (\frac {1}{4}+x+x^2\right )}{x} \, dx \\ \end{align*}

Mathematica [N/A]

Not integrable

Time = 9.94 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.15 \[ \int \frac {\cos \left (\frac {1}{4}+x+x^2\right )}{x} \, dx=\int \frac {\cos \left (\frac {1}{4}+x+x^2\right )}{x} \, dx \]

[In]

Integrate[Cos[1/4 + x + x^2]/x,x]

[Out]

Integrate[Cos[1/4 + x + x^2]/x, x]

Maple [N/A] (verified)

Not integrable

Time = 0.18 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.85

\[\int \frac {\cos \left (\frac {1}{4}+x +x^{2}\right )}{x}d x\]

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.27 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00 \[ \int \frac {\cos \left (\frac {1}{4}+x+x^2\right )}{x} \, dx=\int { \frac {\cos \left (x^{2} + x + \frac {1}{4}\right )}{x} \,d x } \]

[In]

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

[Out]

integral(cos(x^2 + x + 1/4)/x, x)

Sympy [N/A]

Not integrable

Time = 0.35 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.92 \[ \int \frac {\cos \left (\frac {1}{4}+x+x^2\right )}{x} \, dx=\int \frac {\cos {\left (x^{2} + x + \frac {1}{4} \right )}}{x}\, dx \]

[In]

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

[Out]

Integral(cos(x**2 + x + 1/4)/x, x)

Maxima [N/A]

Not integrable

Time = 0.35 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00 \[ \int \frac {\cos \left (\frac {1}{4}+x+x^2\right )}{x} \, dx=\int { \frac {\cos \left (x^{2} + x + \frac {1}{4}\right )}{x} \,d x } \]

[In]

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

[Out]

integrate(cos(x^2 + x + 1/4)/x, x)

Giac [N/A]

Not integrable

Time = 0.41 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00 \[ \int \frac {\cos \left (\frac {1}{4}+x+x^2\right )}{x} \, dx=\int { \frac {\cos \left (x^{2} + x + \frac {1}{4}\right )}{x} \,d x } \]

[In]

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

[Out]

integrate(cos(x^2 + x + 1/4)/x, x)

Mupad [N/A]

Not integrable

Time = 13.77 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00 \[ \int \frac {\cos \left (\frac {1}{4}+x+x^2\right )}{x} \, dx=\int \frac {\cos \left (x^2+x+\frac {1}{4}\right )}{x} \,d x \]

[In]

int(cos(x + x^2 + 1/4)/x,x)

[Out]

int(cos(x + x^2 + 1/4)/x, x)