Optimal. Leaf size=14 \[ \frac {1}{8} x^7 \sqrt {x^2} \]
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Rubi [A] time = 0.00, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.286, Rules used = {15, 30} \begin {gather*} \frac {1}{8} x^7 \sqrt {x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int \left (x^2\right )^{7/2} \, dx &=\frac {\sqrt {x^2} \int x^7 \, dx}{x}\\ &=\frac {1}{8} x^7 \sqrt {x^2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 12, normalized size = 0.86 \begin {gather*} \frac {1}{8} x \left (x^2\right )^{7/2} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 1.51, size = 12, normalized size = 0.86 \begin {gather*} \frac {1}{8} x \left (x^2\right )^{7/2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.85, size = 5, normalized size = 0.36 \begin {gather*} \frac {1}{8} \, x^{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.41, size = 7, normalized size = 0.50 \begin {gather*} \frac {1}{8} \, x^{8} \mathrm {sgn}\relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 9, normalized size = 0.64 \begin {gather*} \frac {\left (x^{2}\right )^{\frac {7}{2}} x}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.30, size = 8, normalized size = 0.57 \begin {gather*} \frac {1}{8} \, {\left (x^{2}\right )}^{\frac {7}{2}} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.07 \begin {gather*} \int {\left (x^2\right )}^{7/2} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 3, normalized size = 0.21 \begin {gather*} \frac {x^{8}}{8} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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