Optimal. Leaf size=18 \[ 3 \sin ^{-1}(x)-\sqrt {1-x^2} \]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 18, normalized size of antiderivative = 1.00, 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} \begin {gather*} 3 \sin ^{-1}(x)-\sqrt {1-x^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 216
Rule 641
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 = 0.01, size = 18, normalized size = 1.00 \begin {gather*} 3 \sin ^{-1}(x)-\sqrt {1-x^2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [A] time = 0.16, size = 34, normalized size = 1.89 \begin {gather*} -\sqrt {1-x^2}-6 \tan ^{-1}\left (\frac {\sqrt {1-x^2}}{x+1}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.40, size = 30, normalized size = 1.67 \begin {gather*} -\sqrt {-x^{2} + 1} - 6 \, \arctan \left (\frac {\sqrt {-x^{2} + 1} - 1}{x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.22, size = 16, normalized size = 0.89 \begin {gather*} -\sqrt {-x^{2} + 1} + 3 \, \arcsin \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.05, size = 17, normalized size = 0.94 \begin {gather*} 3 \arcsin \relax (x )-\sqrt {-x^{2}+1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 2.87, size = 16, normalized size = 0.89 \begin {gather*} -\sqrt {-x^{2} + 1} + 3 \, \arcsin \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.33, size = 16, normalized size = 0.89 \begin {gather*} 3\,\mathrm {asin}\relax (x)-\sqrt {1-x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.15, size = 12, normalized size = 0.67 \begin {gather*} - \sqrt {1 - x^{2}} + 3 \operatorname {asin}{\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________