\(\int \frac {\sin (a+b x) \text {Si}(c+d x)}{x} \, dx\) [65]

Optimal result

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

[Out]

CannotIntegrate(Si(d*x+c)*sin(b*x+a)/x,x)

Rubi [N/A]

Not integrable

Time = 0.12 (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 = {} \[ \int \frac {\sin (a+b x) \text {Si}(c+d x)}{x} \, dx=\int \frac {\sin (a+b x) \text {Si}(c+d x)}{x} \, dx \]

[In]

Int[(Sin[a + b*x]*SinIntegral[c + d*x])/x,x]

[Out]

Defer[Int][(Sin[a + b*x]*SinIntegral[c + d*x])/x, x]

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

Mathematica [N/A]

Not integrable

Time = 13.37 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\sin (a+b x) \text {Si}(c+d x)}{x} \, dx=\int \frac {\sin (a+b x) \text {Si}(c+d x)}{x} \, dx \]

[In]

Integrate[(Sin[a + b*x]*SinIntegral[c + d*x])/x,x]

[Out]

Integrate[(Sin[a + b*x]*SinIntegral[c + d*x])/x, x]

Maple [N/A] (verified)

Not integrable

Time = 0.35 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00

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

[In]

int(Si(d*x+c)*sin(b*x+a)/x,x)

[Out]

int(Si(d*x+c)*sin(b*x+a)/x,x)

Fricas [N/A]

Not integrable

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

[In]

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

[Out]

integral(sin(b*x + a)*sin_integral(d*x + c)/x, x)

Sympy [N/A]

Not integrable

Time = 0.75 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.94 \[ \int \frac {\sin (a+b x) \text {Si}(c+d x)}{x} \, dx=\int \frac {\sin {\left (a + b x \right )} \operatorname {Si}{\left (c + d x \right )}}{x}\, dx \]

[In]

integrate(Si(d*x+c)*sin(b*x+a)/x,x)

[Out]

Integral(sin(a + b*x)*Si(c + d*x)/x, x)

Maxima [N/A]

Not integrable

Time = 0.38 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\sin (a+b x) \text {Si}(c+d x)}{x} \, dx=\int { \frac {\sin \left (b x + a\right ) \operatorname {Si}\left (d x + c\right )}{x} \,d x } \]

[In]

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

[Out]

integrate(sin(b*x + a)*sin_integral(d*x + c)/x, x)

Giac [N/A]

Not integrable

Time = 0.30 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\sin (a+b x) \text {Si}(c+d x)}{x} \, dx=\int { \frac {\sin \left (b x + a\right ) \operatorname {Si}\left (d x + c\right )}{x} \,d x } \]

[In]

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

[Out]

integrate(sin(b*x + a)*sin_integral(d*x + c)/x, x)

Mupad [N/A]

Not integrable

Time = 6.59 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int \frac {\sin (a+b x) \text {Si}(c+d x)}{x} \, dx=\int \frac {\mathrm {sinint}\left (c+d\,x\right )\,\sin \left (a+b\,x\right )}{x} \,d x \]

[In]

int((sinint(c + d*x)*sin(a + b*x))/x,x)

[Out]

int((sinint(c + d*x)*sin(a + b*x))/x, x)