Optimal. Leaf size=14 \[ \sin (x+1)-(x+1) \cos (x+1) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0111327, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25, Rules used = {3296, 2637} \[ \sin (x+1)-(x+1) \cos (x+1) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 3296
Rule 2637
Rubi steps
\begin{align*} \int (1+x) \sin (1+x) \, dx &=-(1+x) \cos (1+x)+\int \cos (1+x) \, dx\\ &=-(1+x) \cos (1+x)+\sin (1+x)\\ \end{align*}
Mathematica [A] time = 0.0300698, size = 14, normalized size = 1. \[ \sin (x+1)-(x+1) \cos (x+1) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.006, size = 15, normalized size = 1.1 \begin{align*} - \left ( 1+x \right ) \cos \left ( 1+x \right ) +\sin \left ( 1+x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.965903, size = 19, normalized size = 1.36 \begin{align*} -{\left (x + 1\right )} \cos \left (x + 1\right ) + \sin \left (x + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.95472, size = 46, normalized size = 3.29 \begin{align*} -{\left (x + 1\right )} \cos \left (x + 1\right ) + \sin \left (x + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.170035, size = 15, normalized size = 1.07 \begin{align*} - x \cos{\left (x + 1 \right )} + \sin{\left (x + 1 \right )} - \cos{\left (x + 1 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.08431, size = 19, normalized size = 1.36 \begin{align*} -{\left (x + 1\right )} \cos \left (x + 1\right ) + \sin \left (x + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]