Optimal. Leaf size=17 \[ -\frac {\sin ^{-1}\left (\frac {1}{7} (5-6 x)\right )}{\sqrt {3}} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {633, 222}
\begin {gather*} -\frac {\text {ArcSin}\left (\frac {1}{7} (5-6 x)\right )}{\sqrt {3}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 222
Rule 633
Rubi steps
\begin {align*} \int \frac {1}{\sqrt {2+5 x-3 x^2}} \, dx &=-\frac {\text {Subst}\left (\int \frac {1}{\sqrt {1-\frac {x^2}{49}}} \, dx,x,5-6 x\right )}{7 \sqrt {3}}\\ &=-\frac {\sin ^{-1}\left (\frac {1}{7} (5-6 x)\right )}{\sqrt {3}}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.06, size = 30, normalized size = 1.76 \begin {gather*} -\frac {2 \tan ^{-1}\left (\frac {\sqrt {6+15 x-9 x^2}}{1+3 x}\right )}{\sqrt {3}} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.49, size = 12, normalized size = 0.71
method | result | size |
default | \(\frac {\arcsin \left (-\frac {5}{7}+\frac {6 x}{7}\right ) \sqrt {3}}{3}\) | \(12\) |
trager | \(-\frac {\RootOf \left (\textit {\_Z}^{2}+3\right ) \ln \left (6 x \RootOf \left (\textit {\_Z}^{2}+3\right )+6 \sqrt {-3 x^{2}+5 x +2}-5 \RootOf \left (\textit {\_Z}^{2}+3\right )\right )}{3}\) | \(42\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.53, size = 11, normalized size = 0.65 \begin {gather*} -\frac {1}{3} \, \sqrt {3} \arcsin \left (-\frac {6}{7} \, x + \frac {5}{7}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 40 vs.
\(2 (11) = 22\).
time = 1.27, size = 40, normalized size = 2.35 \begin {gather*} -\frac {1}{3} \, \sqrt {3} \arctan \left (\frac {\sqrt {3} \sqrt {-3 \, x^{2} + 5 \, x + 2} {\left (6 \, x - 5\right )}}{6 \, {\left (3 \, x^{2} - 5 \, x - 2\right )}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{\sqrt {- 3 x^{2} + 5 x + 2}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 31 vs.
\(2 (11) = 22\).
time = 0.90, size = 31, normalized size = 1.82 \begin {gather*} \frac {1}{12} \, \sqrt {-3 \, x^{2} + 5 \, x + 2} {\left (6 \, x - 5\right )} + \frac {49}{72} \, \sqrt {3} \arcsin \left (\frac {6}{7} \, x - \frac {5}{7}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.17, size = 11, normalized size = 0.65 \begin {gather*} \frac {\sqrt {3}\,\mathrm {asin}\left (\frac {6\,x}{7}-\frac {5}{7}\right )}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________