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

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

[Out]

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

________________________________________________________________________________________

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 = {} \begin {gather*} \int \frac {\cos \left ((a+b x)^2\right )}{x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[Cos[(a + b*x)^2]/x,x]

[Out]

Defer[Int][Cos[(a + b*x)^2]/x, x]

Rubi steps

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

________________________________________________________________________________________

Mathematica [A]
time = 2.70, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\cos \left ((a+b x)^2\right )}{x} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[Cos[(a + b*x)^2]/x,x]

[Out]

Integrate[Cos[(a + b*x)^2]/x, x]

________________________________________________________________________________________

Maple [A]
time = 0.05, size = 0, normalized size = 0.00 \[\int \frac {\cos \left (\left (b x +a \right )^{2}\right )}{x}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(cos((b*x + a)^2)/x, x)

________________________________________________________________________________________

Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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 [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\cos {\left (a^{2} + 2 a b x + b^{2} x^{2} \right )}}{x}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(cos((b*x + a)^2)/x, x)

________________________________________________________________________________________

Mupad [A]
time = 0.00, size = -1, normalized size = -0.07 \begin {gather*} \int \frac {\cos \left ({\left (a+b\,x\right )}^2\right )}{x} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(cos((a + b*x)^2)/x,x)

[Out]

int(cos((a + b*x)^2)/x, x)

________________________________________________________________________________________