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]
________________________________________________________________________________________
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]
[Out]
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*}
________________________________________________________________________________________
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]
[Out]
________________________________________________________________________________________
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]
[Out]
________________________________________________________________________________________
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]
[Out]
________________________________________________________________________________________
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]
[Out]
________________________________________________________________________________________
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]
[Out]
________________________________________________________________________________________
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]
[Out]
________________________________________________________________________________________
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]
[Out]
________________________________________________________________________________________