3.85 \(\int x^m \text{CosIntegral}(a+b x) \, dx\)

Optimal. Leaf size=47 \[ \frac{x^{m+1} \text{CosIntegral}(a+b x)}{m+1}-\frac{b \text{CannotIntegrate}\left (\frac{x^{m+1} \cos (a+b x)}{a+b x},x\right )}{m+1} \]

[Out]

-((b*CannotIntegrate[(x^(1 + m)*Cos[a + b*x])/(a + b*x), x])/(1 + m)) + (x^(1 + m)*CosIntegral[a + b*x])/(1 +
m)

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Rubi [A]  time = 0.315771, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int x^m \text{CosIntegral}(a+b x) \, dx \]

Verification is Not applicable to the result.

[In]

Int[x^m*CosIntegral[a + b*x],x]

[Out]

(x^(1 + m)*CosIntegral[a + b*x])/(1 + m) - (b*Defer[Int][(x^(1 + m)*Cos[a + b*x])/(a + b*x), x])/(1 + m)

Rubi steps

\begin{align*} \int x^m \text{Ci}(a+b x) \, dx &=\frac{x^{1+m} \text{Ci}(a+b x)}{1+m}-\frac{b \int \frac{x^{1+m} \cos (a+b x)}{a+b x} \, dx}{1+m}\\ \end{align*}

Mathematica [A]  time = 3.60651, size = 0, normalized size = 0. \[ \int x^m \text{CosIntegral}(a+b x) \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[x^m*CosIntegral[a + b*x],x]

[Out]

Integrate[x^m*CosIntegral[a + b*x], x]

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Maple [A]  time = 0.155, size = 0, normalized size = 0. \begin{align*} \int{x}^{m}{\it Ci} \left ( bx+a \right ) \, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^m*Ci(b*x+a),x)

[Out]

int(x^m*Ci(b*x+a),x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int x^{m}{\rm Ci}\left (b x + a\right )\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^m*Ci(b*x+a),x, algorithm="maxima")

[Out]

integrate(x^m*Ci(b*x + a), x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (x^{m} \operatorname{Ci}\left (b x + a\right ), x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^m*Ci(b*x+a),x, algorithm="fricas")

[Out]

integral(x^m*cos_integral(b*x + a), x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int x^{m} \operatorname{Ci}{\left (a + b x \right )}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**m*Ci(b*x+a),x)

[Out]

Integral(x**m*Ci(a + b*x), x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int x^{m}{\rm Ci}\left (b x + a\right )\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^m*Ci(b*x+a),x, algorithm="giac")

[Out]

integrate(x^m*Ci(b*x + a), x)