3.17 \(\int x^m \text {Si}(a+b x) \, dx\)

Optimal. Leaf size=48 \[ \frac {x^{m+1} \text {Si}(a+b x)}{m+1}-\frac {b \text {Int}\left (\frac {x^{m+1} \sin (a+b x)}{a+b x},x\right )}{m+1} \]

[Out]

-b*CannotIntegrate(x^(1+m)*sin(b*x+a)/(b*x+a),x)/(1+m)+x^(1+m)*Si(b*x+a)/(1+m)

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Rubi [A]  time = 0.29, 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 = {} \[ \int x^m \text {Si}(a+b x) \, dx \]

Verification is Not applicable to the result.

[In]

Int[x^m*SinIntegral[a + b*x],x]

[Out]

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

Rubi steps

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

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Mathematica [A]  time = 4.77, size = 0, normalized size = 0.00 \[ \int x^m \text {Si}(a+b x) \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[x^m*SinIntegral[a + b*x],x]

[Out]

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

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fricas [A]  time = 2.05, size = 0, normalized size = 0.00 \[ {\rm integral}\left (x^{m} \operatorname {Si}\left (b x + a\right ), x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(x^m*Si(b*x + a), x)

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maple [A]  time = 0.05, size = 0, normalized size = 0.00 \[ \int x^{m} \Si \left (b x +a \right )\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

integrate(x^m*Si(b*x + a), x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.02 \[ \int x^m\,\mathrm {sinint}\left (a+b\,x\right ) \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^m*sinint(a + b*x),x)

[Out]

int(x^m*sinint(a + b*x), x)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Integral(x**m*Si(a + b*x), x)

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