Optimal. Leaf size=10 \[ -\frac{1}{2} \cos \left (x^2+1\right ) \]
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Rubi [A] time = 0.0093647, antiderivative size = 10, 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 = {3379, 2638} \[ -\frac{1}{2} \cos \left (x^2+1\right ) \]
Antiderivative was successfully verified.
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Rule 3379
Rule 2638
Rubi steps
\begin{align*} \int x \sin \left (1+x^2\right ) \, dx &=\frac{1}{2} \operatorname{Subst}\left (\int \sin (1+x) \, dx,x,x^2\right )\\ &=-\frac{1}{2} \cos \left (1+x^2\right )\\ \end{align*}
Mathematica [B] time = 0.013242, size = 21, normalized size = 2.1 \[ \frac{1}{2} \sin (1) \sin \left (x^2\right )-\frac{1}{2} \cos (1) \cos \left (x^2\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 9, normalized size = 0.9 \begin{align*} -{\frac{\cos \left ({x}^{2}+1 \right ) }{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.961171, size = 11, normalized size = 1.1 \begin{align*} -\frac{1}{2} \, \cos \left (x^{2} + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.01179, size = 26, normalized size = 2.6 \begin{align*} -\frac{1}{2} \, \cos \left (x^{2} + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.168666, size = 8, normalized size = 0.8 \begin{align*} - \frac{\cos{\left (x^{2} + 1 \right )}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.072, size = 11, normalized size = 1.1 \begin{align*} -\frac{1}{2} \, \cos \left (x^{2} + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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