Optimal. Leaf size=17 \[ -\frac{\cos ^8\left (a+b x^3\right )}{24 b} \]
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Rubi [A] time = 0.0241569, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045, Rules used = {3442} \[ -\frac{\cos ^8\left (a+b x^3\right )}{24 b} \]
Antiderivative was successfully verified.
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Rule 3442
Rubi steps
\begin{align*} \int x^2 \cos ^7\left (a+b x^3\right ) \sin \left (a+b x^3\right ) \, dx &=-\frac{\cos ^8\left (a+b x^3\right )}{24 b}\\ \end{align*}
Mathematica [A] time = 0.0211926, size = 17, normalized size = 1. \[ -\frac{\cos ^8\left (a+b x^3\right )}{24 b} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 16, normalized size = 0.9 \begin{align*} -{\frac{ \left ( \cos \left ( b{x}^{3}+a \right ) \right ) ^{8}}{24\,b}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.959524, size = 20, normalized size = 1.18 \begin{align*} -\frac{\cos \left (b x^{3} + a\right )^{8}}{24 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.22122, size = 35, normalized size = 2.06 \begin{align*} -\frac{\cos \left (b x^{3} + a\right )^{8}}{24 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 30.8132, size = 27, normalized size = 1.59 \begin{align*} \begin{cases} - \frac{\cos ^{8}{\left (a + b x^{3} \right )}}{24 b} & \text{for}\: b \neq 0 \\\frac{x^{3} \sin{\left (a \right )} \cos ^{7}{\left (a \right )}}{3} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.1732, size = 20, normalized size = 1.18 \begin{align*} -\frac{\cos \left (b x^{3} + a\right )^{8}}{24 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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