Optimal. Leaf size=8 \[ \frac {\sinh \left (x^3\right )}{3} \]
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Rubi [A]
time = 0.01, antiderivative size = 8, 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 = {5429, 2717}
\begin {gather*} \frac {\sinh \left (x^3\right )}{3} \end {gather*}
Antiderivative was successfully verified.
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Rule 2717
Rule 5429
Rubi steps
\begin {align*} \int x^2 \cosh \left (x^3\right ) \, dx &=\frac {1}{3} \text {Subst}\left (\int \cosh (x) \, dx,x,x^3\right )\\ &=\frac {\sinh \left (x^3\right )}{3}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 8, normalized size = 1.00 \begin {gather*} \frac {\sinh \left (x^3\right )}{3} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.46, size = 7, normalized size = 0.88
method | result | size |
derivativedivides | \(\frac {\sinh \left (x^{3}\right )}{3}\) | \(7\) |
default | \(\frac {\sinh \left (x^{3}\right )}{3}\) | \(7\) |
meijerg | \(\frac {\sinh \left (x^{3}\right )}{3}\) | \(7\) |
risch | \(\frac {{\mathrm e}^{x^{3}}}{6}-\frac {{\mathrm e}^{-x^{3}}}{6}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 6, normalized size = 0.75 \begin {gather*} \frac {1}{3} \, \sinh \left (x^{3}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 6, normalized size = 0.75 \begin {gather*} \frac {1}{3} \, \sinh \left (x^{3}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.12, size = 5, normalized size = 0.62 \begin {gather*} \frac {\sinh {\left (x^{3} \right )}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 15 vs.
\(2 (6) = 12\).
time = 0.42, size = 15, normalized size = 1.88 \begin {gather*} -\frac {1}{6} \, e^{\left (-x^{3}\right )} + \frac {1}{6} \, e^{\left (x^{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.88, size = 6, normalized size = 0.75 \begin {gather*} \frac {\mathrm {sinh}\left (x^3\right )}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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