3.58 \(\int \frac {\sin (a+b x) \text {Si}(a+b x)}{x} \, dx\)

Optimal. Leaf size=19 \[ \text {Int}\left (\frac {\text {Si}(a+b x) \sin (a+b x)}{x},x\right ) \]

[Out]

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

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Rubi [A]  time = 0.12, 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 = {} \[ \int \frac {\sin (a+b x) \text {Si}(a+b x)}{x} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

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Mathematica [A]  time = 5.33, size = 0, normalized size = 0.00 \[ \int \frac {\sin (a+b x) \text {Si}(a+b x)}{x} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 0.88, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\sin \left (b x + a\right ) \operatorname {Si}\left (b x + a\right )}{x}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(Si(b*x+a)*sin(b*x+a)/x,x, algorithm="fricas")

[Out]

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

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\rm Si}\left (b x + a\right ) \sin \left (b x + a\right )}{x}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(Si(b*x+a)*sin(b*x+a)/x,x, algorithm="giac")

[Out]

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

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maple [A]  time = 0.03, size = 0, normalized size = 0.00 \[ \int \frac {\Si \left (b x +a \right ) \sin \left (b x +a \right )}{x}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\rm Si}\left (b x + a\right ) \sin \left (b x + a\right )}{x}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(Si(b*x+a)*sin(b*x+a)/x,x, algorithm="maxima")

[Out]

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

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mupad [A]  time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {\mathrm {sinint}\left (a+b\,x\right )\,\sin \left (a+b\,x\right )}{x} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\sin {\left (a + b x \right )} \operatorname {Si}{\left (a + b x \right )}}{x}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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