Optimal. Leaf size=10 \[ -\frac {1}{2} \cos \left (x^2+1\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {3379, 2638} \[ -\frac {1}{2} \cos \left (x^2+1\right ) \]
Antiderivative was successfully verified.
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Rule 2638
Rule 3379
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*}
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Mathematica [B] time = 0.01, size = 21, normalized size = 2.10 \[ \frac {1}{2} \sin (1) \sin \left (x^2\right )-\frac {1}{2} \cos (1) \cos \left (x^2\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.71, size = 8, normalized size = 0.80 \[ -\frac {1}{2} \, \cos \left (x^{2} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.12, size = 8, normalized size = 0.80 \[ -\frac {1}{2} \, \cos \left (x^{2} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 9, normalized size = 0.90 \[ -\frac {\cos \left (x^{2}+1\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.32, size = 8, normalized size = 0.80 \[ -\frac {1}{2} \, \cos \left (x^{2} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 8, normalized size = 0.80 \[ -\frac {\cos \left (x^2+1\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 8, normalized size = 0.80 \[ - \frac {\cos {\left (x^{2} + 1 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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