Optimal. Leaf size=18 \[ 3 \sin ^{-1}(x)-\sqrt{1-x^2} \]
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Rubi [A] time = 0.0049978, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133, Rules used = {641, 216} \[ 3 \sin ^{-1}(x)-\sqrt{1-x^2} \]
Antiderivative was successfully verified.
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Rule 641
Rule 216
Rubi steps
\begin{align*} \int \frac{3+x}{\sqrt{1-x^2}} \, dx &=-\sqrt{1-x^2}+3 \int \frac{1}{\sqrt{1-x^2}} \, dx\\ &=-\sqrt{1-x^2}+3 \sin ^{-1}(x)\\ \end{align*}
Mathematica [A] time = 0.0107118, size = 18, normalized size = 1. \[ 3 \sin ^{-1}(x)-\sqrt{1-x^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.043, size = 17, normalized size = 0.9 \begin{align*} 3\,\arcsin \left ( x \right ) -\sqrt{-{x}^{2}+1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.74777, size = 22, normalized size = 1.22 \begin{align*} -\sqrt{-x^{2} + 1} + 3 \, \arcsin \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.72906, size = 70, normalized size = 3.89 \begin{align*} -\sqrt{-x^{2} + 1} - 6 \, \arctan \left (\frac{\sqrt{-x^{2} + 1} - 1}{x}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.136026, size = 12, normalized size = 0.67 \begin{align*} - \sqrt{1 - x^{2}} + 3 \operatorname{asin}{\left (x \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.38096, size = 22, normalized size = 1.22 \begin{align*} -\sqrt{-x^{2} + 1} + 3 \, \arcsin \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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