\(\int \frac {\cos (a+b x) \operatorname {CosIntegral}(c+d x)}{x} \, dx\) [136]

Optimal result

Integrand size = 16, antiderivative size = 16 \[ \int \frac {\cos (a+b x) \operatorname {CosIntegral}(c+d x)}{x} \, dx=\text {Int}\left (\frac {\cos (a+b x) \operatorname {CosIntegral}(c+d x)}{x},x\right ) \]

[Out]

CannotIntegrate(Ci(d*x+c)*cos(b*x+a)/x,x)

Rubi [N/A]

Not integrable

Time = 0.08 (sec) , antiderivative size = 16, 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 = {} \[ \int \frac {\cos (a+b x) \operatorname {CosIntegral}(c+d x)}{x} \, dx=\int \frac {\cos (a+b x) \operatorname {CosIntegral}(c+d x)}{x} \, dx \]

[In]

Int[(Cos[a + b*x]*CosIntegral[c + d*x])/x,x]

[Out]

Defer[Int][(Cos[a + b*x]*CosIntegral[c + d*x])/x, x]

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

Mathematica [N/A]

Not integrable

Time = 9.20 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\cos (a+b x) \operatorname {CosIntegral}(c+d x)}{x} \, dx=\int \frac {\cos (a+b x) \operatorname {CosIntegral}(c+d x)}{x} \, dx \]

[In]

Integrate[(Cos[a + b*x]*CosIntegral[c + d*x])/x,x]

[Out]

Integrate[(Cos[a + b*x]*CosIntegral[c + d*x])/x, x]

Maple [N/A] (verified)

Not integrable

Time = 0.34 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00

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

[In]

int(Ci(d*x+c)*cos(b*x+a)/x,x)

[Out]

int(Ci(d*x+c)*cos(b*x+a)/x,x)

Fricas [N/A]

Not integrable

Time = 0.25 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\cos (a+b x) \operatorname {CosIntegral}(c+d x)}{x} \, dx=\int { \frac {\cos \left (b x + a\right ) \operatorname {C}\left (d x + c\right )}{x} \,d x } \]

[In]

integrate(fresnel_cos(d*x+c)*cos(b*x+a)/x,x, algorithm="fricas")

[Out]

integral(cos(b*x + a)*fresnel_cos(d*x + c)/x, x)

Sympy [N/A]

Not integrable

Time = 0.69 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.94 \[ \int \frac {\cos (a+b x) \operatorname {CosIntegral}(c+d x)}{x} \, dx=\int \frac {\cos {\left (a + b x \right )} \operatorname {Ci}{\left (c + d x \right )}}{x}\, dx \]

[In]

integrate(Ci(d*x+c)*cos(b*x+a)/x,x)

[Out]

Integral(cos(a + b*x)*Ci(c + d*x)/x, x)

Maxima [N/A]

Not integrable

Time = 0.37 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\cos (a+b x) \operatorname {CosIntegral}(c+d x)}{x} \, dx=\int { \frac {\cos \left (b x + a\right ) \operatorname {C}\left (d x + c\right )}{x} \,d x } \]

[In]

integrate(fresnel_cos(d*x+c)*cos(b*x+a)/x,x, algorithm="maxima")

[Out]

integrate(cos(b*x + a)*fresnel_cos(d*x + c)/x, x)

Giac [N/A]

Not integrable

Time = 0.27 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\cos (a+b x) \operatorname {CosIntegral}(c+d x)}{x} \, dx=\int { \frac {\cos \left (b x + a\right ) \operatorname {C}\left (d x + c\right )}{x} \,d x } \]

[In]

integrate(fresnel_cos(d*x+c)*cos(b*x+a)/x,x, algorithm="giac")

[Out]

integrate(cos(b*x + a)*fresnel_cos(d*x + c)/x, x)

Mupad [N/A]

Not integrable

Time = 5.20 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\cos (a+b x) \operatorname {CosIntegral}(c+d x)}{x} \, dx=\int \frac {\mathrm {cosint}\left (c+d\,x\right )\,\cos \left (a+b\,x\right )}{x} \,d x \]

[In]

int((cosint(c + d*x)*cos(a + b*x))/x,x)

[Out]

int((cosint(c + d*x)*cos(a + b*x))/x, x)