Optimal. Leaf size=10 \[ \frac{\sin \left (x^3\right )}{3}+x \]
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Rubi [A] time = 0.0098915, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2, Rules used = {3380, 2637} \[ \frac{\sin \left (x^3\right )}{3}+x \]
Antiderivative was successfully verified.
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Rule 3380
Rule 2637
Rubi steps
\begin{align*} \int \left (1+x^2 \cos \left (x^3\right )\right ) \, dx &=x+\int x^2 \cos \left (x^3\right ) \, dx\\ &=x+\frac{1}{3} \operatorname{Subst}\left (\int \cos (x) \, dx,x,x^3\right )\\ &=x+\frac{\sin \left (x^3\right )}{3}\\ \end{align*}
Mathematica [A] time = 0.0027596, size = 10, normalized size = 1. \[ \frac{\sin \left (x^3\right )}{3}+x \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 9, normalized size = 0.9 \begin{align*} x+{\frac{\sin \left ({x}^{3} \right ) }{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.949289, size = 11, normalized size = 1.1 \begin{align*} x + \frac{1}{3} \, \sin \left (x^{3}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.05855, size = 24, normalized size = 2.4 \begin{align*} x + \frac{1}{3} \, \sin \left (x^{3}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.297757, size = 7, normalized size = 0.7 \begin{align*} x + \frac{\sin{\left (x^{3} \right )}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.0812, size = 11, normalized size = 1.1 \begin{align*} x + \frac{1}{3} \, \sin \left (x^{3}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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