\(\int \frac {\cos ((a+b x)^2)}{x} \, dx\) [88]

Optimal result

Integrand size = 12, antiderivative size = 12 \[ \int \frac {\cos \left ((a+b x)^2\right )}{x} \, dx=\text {Int}\left (\frac {\cos \left ((a+b x)^2\right )}{x},x\right ) \]

[Out]

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

Rubi [N/A]

Not integrable

Time = 0.01 (sec) , antiderivative size = 12, 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 = {} \[ \int \frac {\cos \left ((a+b x)^2\right )}{x} \, dx=\int \frac {\cos \left ((a+b x)^2\right )}{x} \, dx \]

[In]

Int[Cos[(a + b*x)^2]/x,x]

[Out]

Defer[Int][Cos[(a + b*x)^2]/x, x]

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

Mathematica [N/A]

Not integrable

Time = 2.30 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {\cos \left ((a+b x)^2\right )}{x} \, dx=\int \frac {\cos \left ((a+b x)^2\right )}{x} \, dx \]

[In]

Integrate[Cos[(a + b*x)^2]/x,x]

[Out]

Integrate[Cos[(a + b*x)^2]/x, x]

Maple [N/A] (verified)

Not integrable

Time = 0.15 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00

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

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.25 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.92 \[ \int \frac {\cos \left ((a+b x)^2\right )}{x} \, dx=\int { \frac {\cos \left ({\left (b x + a\right )}^{2}\right )}{x} \,d x } \]

[In]

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

[Out]

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

Sympy [N/A]

Not integrable

Time = 0.99 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.67 \[ \int \frac {\cos \left ((a+b x)^2\right )}{x} \, dx=\int \frac {\cos {\left (a^{2} + 2 a b x + b^{2} x^{2} \right )}}{x}\, dx \]

[In]

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

[Out]

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

Maxima [N/A]

Not integrable

Time = 0.42 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {\cos \left ((a+b x)^2\right )}{x} \, dx=\int { \frac {\cos \left ({\left (b x + a\right )}^{2}\right )}{x} \,d x } \]

[In]

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

[Out]

integrate(cos((b*x + a)^2)/x, x)

Giac [N/A]

Not integrable

Time = 0.31 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {\cos \left ((a+b x)^2\right )}{x} \, dx=\int { \frac {\cos \left ({\left (b x + a\right )}^{2}\right )}{x} \,d x } \]

[In]

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

[Out]

integrate(cos((b*x + a)^2)/x, x)

Mupad [N/A]

Not integrable

Time = 13.15 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {\cos \left ((a+b x)^2\right )}{x} \, dx=\int \frac {\cos \left ({\left (a+b\,x\right )}^2\right )}{x} \,d x \]

[In]

int(cos((a + b*x)^2)/x,x)

[Out]

int(cos((a + b*x)^2)/x, x)