\(\int \frac {\operatorname {CosIntegral}(b x) \sin (b x)}{x} \, dx\) [109]

Optimal result

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

[Out]

CannotIntegrate(Ci(b*x)*sin(b*x)/x,x)

Rubi [N/A]

Not integrable

Time = 0.02 (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 = {} \[ \int \frac {\operatorname {CosIntegral}(b x) \sin (b x)}{x} \, dx=\int \frac {\operatorname {CosIntegral}(b x) \sin (b x)}{x} \, dx \]

[In]

Int[(CosIntegral[b*x]*Sin[b*x])/x,x]

[Out]

Defer[Int][(CosIntegral[b*x]*Sin[b*x])/x, x]

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

Mathematica [N/A]

Not integrable

Time = 1.45 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {\operatorname {CosIntegral}(b x) \sin (b x)}{x} \, dx=\int \frac {\operatorname {CosIntegral}(b x) \sin (b x)}{x} \, dx \]

[In]

Integrate[(CosIntegral[b*x]*Sin[b*x])/x,x]

[Out]

Integrate[(CosIntegral[b*x]*Sin[b*x])/x, x]

Maple [N/A] (verified)

Not integrable

Time = 0.21 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00

\[\int \frac {\operatorname {Ci}\left (b x \right ) \sin \left (b x \right )}{x}d x\]

[In]

int(Ci(b*x)*sin(b*x)/x,x)

[Out]

int(Ci(b*x)*sin(b*x)/x,x)

Fricas [N/A]

Not integrable

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

[In]

integrate(fresnel_cos(b*x)*sin(b*x)/x,x, algorithm="fricas")

[Out]

integral(fresnel_cos(b*x)*sin(b*x)/x, x)

Sympy [N/A]

Not integrable

Time = 2.12 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {\operatorname {CosIntegral}(b x) \sin (b x)}{x} \, dx=\int \frac {\sin {\left (b x \right )} \operatorname {Ci}{\left (b x \right )}}{x}\, dx \]

[In]

integrate(Ci(b*x)*sin(b*x)/x,x)

[Out]

Integral(sin(b*x)*Ci(b*x)/x, x)

Maxima [N/A]

Not integrable

Time = 0.26 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {\operatorname {CosIntegral}(b x) \sin (b x)}{x} \, dx=\int { \frac {\operatorname {C}\left (b x\right ) \sin \left (b x\right )}{x} \,d x } \]

[In]

integrate(fresnel_cos(b*x)*sin(b*x)/x,x, algorithm="maxima")

[Out]

integrate(fresnel_cos(b*x)*sin(b*x)/x, x)

Giac [N/A]

Not integrable

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

[In]

integrate(fresnel_cos(b*x)*sin(b*x)/x,x, algorithm="giac")

[Out]

integrate(fresnel_cos(b*x)*sin(b*x)/x, x)

Mupad [N/A]

Not integrable

Time = 5.15 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {\operatorname {CosIntegral}(b x) \sin (b x)}{x} \, dx=\int \frac {\mathrm {cosint}\left (b\,x\right )\,\sin \left (b\,x\right )}{x} \,d x \]

[In]

int((cosint(b*x)*sin(b*x))/x,x)

[Out]

int((cosint(b*x)*sin(b*x))/x, x)