Optimal. Leaf size=19 \[ \frac{1}{7} b^2 x^6 \sqrt{b x^2} \]
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Rubi [A] time = 0.0017408, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182, Rules used = {15, 30} \[ \frac{1}{7} b^2 x^6 \sqrt{b x^2} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int x \left (b x^2\right )^{5/2} \, dx &=\frac{\left (b^2 \sqrt{b x^2}\right ) \int x^6 \, dx}{x}\\ &=\frac{1}{7} b^2 x^6 \sqrt{b x^2}\\ \end{align*}
Mathematica [A] time = 0.0017863, size = 16, normalized size = 0.84 \[ \frac{1}{7} x^2 \left (b x^2\right )^{5/2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 13, normalized size = 0.7 \begin{align*}{\frac{{x}^{2}}{7} \left ( b{x}^{2} \right ) ^{{\frac{5}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.06203, size = 16, normalized size = 0.84 \begin{align*} \frac{\left (b x^{2}\right )^{\frac{7}{2}}}{7 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.19325, size = 34, normalized size = 1.79 \begin{align*} \frac{1}{7} \, \sqrt{b x^{2}} b^{2} x^{6} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.40194, size = 15, normalized size = 0.79 \begin{align*} \frac{b^{\frac{5}{2}} x^{2} \left (x^{2}\right )^{\frac{5}{2}}}{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.17067, size = 14, normalized size = 0.74 \begin{align*} \frac{1}{7} \, b^{\frac{5}{2}} x^{7} \mathrm{sgn}\left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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