Optimal. Leaf size=26 \[ \frac{(a+b x) \text{Si}(a+b x)}{b}+\frac{\cos (a+b x)}{b} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0054842, antiderivative size = 26, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 6, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167, Rules used = {6499} \[ \frac{(a+b x) \text{Si}(a+b x)}{b}+\frac{\cos (a+b x)}{b} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 6499
Rubi steps
\begin{align*} \int \text{Si}(a+b x) \, dx &=\frac{\cos (a+b x)}{b}+\frac{(a+b x) \text{Si}(a+b x)}{b}\\ \end{align*}
Mathematica [A] time = 0.0359392, size = 41, normalized size = 1.58 \[ x \text{Si}(a+b x)+\frac{a \text{Si}(a+b x)}{b}-\frac{\sin (a) \sin (b x)}{b}+\frac{\cos (a) \cos (b x)}{b} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.049, size = 24, normalized size = 0.9 \begin{align*}{\frac{ \left ( bx+a \right ){\it Si} \left ( bx+a \right ) +\cos \left ( bx+a \right ) }{b}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int{\rm Si}\left (b x + a\right )\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [F] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\operatorname{Si}\left (b x + a\right ), x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \operatorname{Si}{\left (a + b x \right )}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [C] time = 1.34509, size = 62, normalized size = 2.38 \begin{align*} x \operatorname{Si}\left (b x + a\right ) + \frac{a \Im \left ( \operatorname{Ci}\left (b x + a\right ) \right ) - a \Im \left ( \operatorname{Ci}\left (-b x - a\right ) \right ) + 2 \, a \operatorname{Si}\left (b x + a\right )}{2 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]