Optimal. Leaf size=13 \[ \frac {5}{3} \left (x^2+1\right )^{3/2} \]
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Rubi [A] time = 0.00, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {12, 261} \[ \frac {5}{3} \left (x^2+1\right )^{3/2} \]
Antiderivative was successfully verified.
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Rule 12
Rule 261
Rubi steps
\begin {align*} \int 5 x \sqrt {1+x^2} \, dx &=5 \int x \sqrt {1+x^2} \, dx\\ &=\frac {5}{3} \left (1+x^2\right )^{3/2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 13, normalized size = 1.00 \[ \frac {5}{3} \left (x^2+1\right )^{3/2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 9, normalized size = 0.69 \[ \frac {5}{3} \, {\left (x^{2} + 1\right )}^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.99, size = 9, normalized size = 0.69 \[ \frac {5}{3} \, {\left (x^{2} + 1\right )}^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 10, normalized size = 0.77 \[ \frac {5 \left (x^{2}+1\right )^{\frac {3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 9, normalized size = 0.69 \[ \frac {5}{3} \, {\left (x^{2} + 1\right )}^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 9, normalized size = 0.69 \[ \frac {5\,{\left (x^2+1\right )}^{3/2}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.20, size = 26, normalized size = 2.00 \[ \frac {5 x^{2} \sqrt {x^{2} + 1}}{3} + \frac {5 \sqrt {x^{2} + 1}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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