Integrand size = 8, antiderivative size = 8 \[ \int x^2 \cosh \left (x^3\right ) \, dx=\frac {\sinh \left (x^3\right )}{3} \]
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Time = 0.01 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {5429, 2717} \[ \int x^2 \cosh \left (x^3\right ) \, dx=\frac {\sinh \left (x^3\right )}{3} \]
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Rule 2717
Rule 5429
Rubi steps \begin{align*} \text {integral}& = \frac {1}{3} \text {Subst}\left (\int \cosh (x) \, dx,x,x^3\right ) \\ & = \frac {\sinh \left (x^3\right )}{3} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00 \[ \int x^2 \cosh \left (x^3\right ) \, dx=\frac {\sinh \left (x^3\right )}{3} \]
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Time = 0.05 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.88
method | result | size |
derivativedivides | \(\frac {\sinh \left (x^{3}\right )}{3}\) | \(7\) |
default | \(\frac {\sinh \left (x^{3}\right )}{3}\) | \(7\) |
meijerg | \(\frac {\sinh \left (x^{3}\right )}{3}\) | \(7\) |
parallelrisch | \(\frac {\sinh \left (x^{3}\right )}{3}\) | \(7\) |
risch | \(\frac {{\mathrm e}^{x^{3}}}{6}-\frac {{\mathrm e}^{-x^{3}}}{6}\) | \(16\) |
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none
Time = 0.24 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.75 \[ \int x^2 \cosh \left (x^3\right ) \, dx=\frac {1}{3} \, \sinh \left (x^{3}\right ) \]
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Time = 0.11 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.62 \[ \int x^2 \cosh \left (x^3\right ) \, dx=\frac {\sinh {\left (x^{3} \right )}}{3} \]
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none
Time = 0.18 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.75 \[ \int x^2 \cosh \left (x^3\right ) \, dx=\frac {1}{3} \, \sinh \left (x^{3}\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. 15 vs. \(2 (6) = 12\).
Time = 0.26 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.88 \[ \int x^2 \cosh \left (x^3\right ) \, dx=-\frac {1}{6} \, e^{\left (-x^{3}\right )} + \frac {1}{6} \, e^{\left (x^{3}\right )} \]
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Time = 1.51 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.75 \[ \int x^2 \cosh \left (x^3\right ) \, dx=\frac {\mathrm {sinh}\left (x^3\right )}{3} \]
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