\(\int \frac {\operatorname {CosIntegral}(a+b x)^2}{x} \, dx\) [97]

Optimal result

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

[Out]

CannotIntegrate(Ci(b*x+a)^2/x,x)

Rubi [N/A]

Not integrable

Time = 0.03 (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 = {} \[ \int \frac {\operatorname {CosIntegral}(a+b x)^2}{x} \, dx=\int \frac {\operatorname {CosIntegral}(a+b x)^2}{x} \, dx \]

[In]

Int[CosIntegral[a + b*x]^2/x,x]

[Out]

Defer[Int][CosIntegral[a + b*x]^2/x, x]

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

Mathematica [N/A]

Not integrable

Time = 0.80 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {\operatorname {CosIntegral}(a+b x)^2}{x} \, dx=\int \frac {\operatorname {CosIntegral}(a+b x)^2}{x} \, dx \]

[In]

Integrate[CosIntegral[a + b*x]^2/x,x]

[Out]

Integrate[CosIntegral[a + b*x]^2/x, x]

Maple [N/A] (verified)

Not integrable

Time = 0.10 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00

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

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.25 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {\operatorname {CosIntegral}(a+b x)^2}{x} \, dx=\int { \frac {\operatorname {C}\left (b x + a\right )^{2}}{x} \,d x } \]

[In]

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

[Out]

integral(fresnel_cos(b*x + a)^2/x, x)

Sympy [N/A]

Not integrable

Time = 0.37 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \frac {\operatorname {CosIntegral}(a+b x)^2}{x} \, dx=\int \frac {\operatorname {Ci}^{2}{\left (a + b x \right )}}{x}\, dx \]

[In]

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

[Out]

Integral(Ci(a + b*x)**2/x, x)

Maxima [N/A]

Not integrable

Time = 0.22 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {\operatorname {CosIntegral}(a+b x)^2}{x} \, dx=\int { \frac {\operatorname {C}\left (b x + a\right )^{2}}{x} \,d x } \]

[In]

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

[Out]

integrate(fresnel_cos(b*x + a)^2/x, x)

Giac [N/A]

Not integrable

Time = 0.27 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {\operatorname {CosIntegral}(a+b x)^2}{x} \, dx=\int { \frac {\operatorname {C}\left (b x + a\right )^{2}}{x} \,d x } \]

[In]

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

[Out]

integrate(fresnel_cos(b*x + a)^2/x, x)

Mupad [N/A]

Not integrable

Time = 4.86 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {\operatorname {CosIntegral}(a+b x)^2}{x} \, dx=\int \frac {{\mathrm {cosint}\left (a+b\,x\right )}^2}{x} \,d x \]

[In]

int(cosint(a + b*x)^2/x,x)

[Out]

int(cosint(a + b*x)^2/x, x)