3.130 \(\int \frac {\cos (a+b x) \text {Ci}(a+b x)}{x} \, dx\)

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

[Out]

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

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Rubi [A]  time = 0.07, 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 = {} \[ \int \frac {\cos (a+b x) \text {CosIntegral}(a+b x)}{x} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

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Mathematica [A]  time = 3.41, size = 0, normalized size = 0.00 \[ \int \frac {\cos (a+b x) \text {Ci}(a+b x)}{x} \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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fricas [A]  time = 0.76, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\cos \left (b x + a\right ) \operatorname {Ci}\left (b x + a\right )}{x}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(Ci(b*x+a)*cos(b*x+a)/x,x, algorithm="fricas")

[Out]

integral(cos(b*x + a)*cos_integral(b*x + a)/x, x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(Ci(b*x+a)*cos(b*x+a)/x,x, algorithm="giac")

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(Ci(b*x+a)*cos(b*x+a)/x,x, algorithm="maxima")

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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