Integrand size = 28, antiderivative size = 99 \[ \int \frac {3-x+x^2}{\left (-2-2 x+x^2\right ) \sqrt {-1+x^3}} \, dx=-\frac {1}{6} \sqrt {15+14 \sqrt {3}} \arctan \left (\frac {\sqrt {-3+2 \sqrt {3}} \sqrt {-1+x^3}}{1+x+x^2}\right )-\frac {1}{6} \sqrt {-15+14 \sqrt {3}} \text {arctanh}\left (\frac {\sqrt {3+2 \sqrt {3}} \sqrt {-1+x^3}}{1+x+x^2}\right ) \]
[Out]
Result contains higher order function than in optimal. Order 4 vs. order 3 in optimal.
Time = 0.40 (sec) , antiderivative size = 457, normalized size of antiderivative = 4.62, number of steps used = 13, number of rules used = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.214, Rules used = {6860, 225, 2160, 2165, 212, 209} \[ \int \frac {3-x+x^2}{\left (-2-2 x+x^2\right ) \sqrt {-1+x^3}} \, dx=-\frac {2 \sqrt {2-\sqrt {3}} (1-x) \sqrt {\frac {x^2+x+1}{\left (-x-\sqrt {3}+1\right )^2}} \operatorname {EllipticF}\left (\arcsin \left (\frac {-x+\sqrt {3}+1}{-x-\sqrt {3}+1}\right ),-7+4 \sqrt {3}\right )}{\sqrt [4]{3} \sqrt {-\frac {1-x}{\left (-x-\sqrt {3}+1\right )^2}} \sqrt {x^3-1}}+\frac {\sqrt {14-5 \sqrt {3}} (1-x) \sqrt {\frac {x^2+x+1}{\left (-x-\sqrt {3}+1\right )^2}} \operatorname {EllipticF}\left (\arcsin \left (\frac {-x+\sqrt {3}+1}{-x-\sqrt {3}+1}\right ),-7+4 \sqrt {3}\right )}{2\ 3^{3/4} \sqrt {-\frac {1-x}{\left (-x-\sqrt {3}+1\right )^2}} \sqrt {x^3-1}}+\frac {\sqrt {38-21 \sqrt {3}} (1-x) \sqrt {\frac {x^2+x+1}{\left (-x-\sqrt {3}+1\right )^2}} \operatorname {EllipticF}\left (\arcsin \left (\frac {-x+\sqrt {3}+1}{-x-\sqrt {3}+1}\right ),-7+4 \sqrt {3}\right )}{2\ 3^{3/4} \sqrt {-\frac {1-x}{\left (-x-\sqrt {3}+1\right )^2}} \sqrt {x^3-1}}+\frac {1}{6} \sqrt {15+14 \sqrt {3}} \arctan \left (\frac {\sqrt {2 \sqrt {3}-3} (1-x)}{\sqrt {x^3-1}}\right )+\frac {1}{6} \sqrt {14 \sqrt {3}-15} \text {arctanh}\left (\frac {\sqrt {3+2 \sqrt {3}} (1-x)}{\sqrt {x^3-1}}\right ) \]
[In]
[Out]
Rule 209
Rule 212
Rule 225
Rule 2160
Rule 2165
Rule 6860
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {1}{\sqrt {-1+x^3}}+\frac {5+x}{\left (-2-2 x+x^2\right ) \sqrt {-1+x^3}}\right ) \, dx \\ & = \int \frac {1}{\sqrt {-1+x^3}} \, dx+\int \frac {5+x}{\left (-2-2 x+x^2\right ) \sqrt {-1+x^3}} \, dx \\ & = -\frac {2 \sqrt {2-\sqrt {3}} (1-x) \sqrt {\frac {1+x+x^2}{\left (1-\sqrt {3}-x\right )^2}} \operatorname {EllipticF}\left (\arcsin \left (\frac {1+\sqrt {3}-x}{1-\sqrt {3}-x}\right ),-7+4 \sqrt {3}\right )}{\sqrt [4]{3} \sqrt {-\frac {1-x}{\left (1-\sqrt {3}-x\right )^2}} \sqrt {-1+x^3}}+\int \left (\frac {1+2 \sqrt {3}}{\left (-2-2 \sqrt {3}+2 x\right ) \sqrt {-1+x^3}}+\frac {1-2 \sqrt {3}}{\left (-2+2 \sqrt {3}+2 x\right ) \sqrt {-1+x^3}}\right ) \, dx \\ & = -\frac {2 \sqrt {2-\sqrt {3}} (1-x) \sqrt {\frac {1+x+x^2}{\left (1-\sqrt {3}-x\right )^2}} \operatorname {EllipticF}\left (\arcsin \left (\frac {1+\sqrt {3}-x}{1-\sqrt {3}-x}\right ),-7+4 \sqrt {3}\right )}{\sqrt [4]{3} \sqrt {-\frac {1-x}{\left (1-\sqrt {3}-x\right )^2}} \sqrt {-1+x^3}}+\left (1-2 \sqrt {3}\right ) \int \frac {1}{\left (-2+2 \sqrt {3}+2 x\right ) \sqrt {-1+x^3}} \, dx+\left (1+2 \sqrt {3}\right ) \int \frac {1}{\left (-2-2 \sqrt {3}+2 x\right ) \sqrt {-1+x^3}} \, dx \\ & = -\frac {2 \sqrt {2-\sqrt {3}} (1-x) \sqrt {\frac {1+x+x^2}{\left (1-\sqrt {3}-x\right )^2}} \operatorname {EllipticF}\left (\arcsin \left (\frac {1+\sqrt {3}-x}{1-\sqrt {3}-x}\right ),-7+4 \sqrt {3}\right )}{\sqrt [4]{3} \sqrt {-\frac {1-x}{\left (1-\sqrt {3}-x\right )^2}} \sqrt {-1+x^3}}+\frac {1}{576} \left (-6+\sqrt {3}\right ) \int \frac {96 \left (1+\sqrt {3}\right )-96 x}{\left (-2+2 \sqrt {3}+2 x\right ) \sqrt {-1+x^3}} \, dx+\frac {1}{12} \left (-6+\sqrt {3}\right ) \int \frac {1}{\sqrt {-1+x^3}} \, dx-\frac {1}{576} \left (6+\sqrt {3}\right ) \int \frac {96 \left (1-\sqrt {3}\right )-96 x}{\left (-2-2 \sqrt {3}+2 x\right ) \sqrt {-1+x^3}} \, dx-\frac {1}{12} \left (6+\sqrt {3}\right ) \int \frac {1}{\sqrt {-1+x^3}} \, dx \\ & = \frac {\sqrt {38-21 \sqrt {3}} (1-x) \sqrt {\frac {1+x+x^2}{\left (1-\sqrt {3}-x\right )^2}} \operatorname {EllipticF}\left (\arcsin \left (\frac {1+\sqrt {3}-x}{1-\sqrt {3}-x}\right ),-7+4 \sqrt {3}\right )}{2\ 3^{3/4} \sqrt {-\frac {1-x}{\left (1-\sqrt {3}-x\right )^2}} \sqrt {-1+x^3}}+\frac {\sqrt {14-5 \sqrt {3}} (1-x) \sqrt {\frac {1+x+x^2}{\left (1-\sqrt {3}-x\right )^2}} \operatorname {EllipticF}\left (\arcsin \left (\frac {1+\sqrt {3}-x}{1-\sqrt {3}-x}\right ),-7+4 \sqrt {3}\right )}{2\ 3^{3/4} \sqrt {-\frac {1-x}{\left (1-\sqrt {3}-x\right )^2}} \sqrt {-1+x^3}}-\frac {2 \sqrt {2-\sqrt {3}} (1-x) \sqrt {\frac {1+x+x^2}{\left (1-\sqrt {3}-x\right )^2}} \operatorname {EllipticF}\left (\arcsin \left (\frac {1+\sqrt {3}-x}{1-\sqrt {3}-x}\right ),-7+4 \sqrt {3}\right )}{\sqrt [4]{3} \sqrt {-\frac {1-x}{\left (1-\sqrt {3}-x\right )^2}} \sqrt {-1+x^3}}+\frac {1}{6} \left (6-\sqrt {3}\right ) \text {Subst}\left (\int \frac {1}{1-\left (3-2 \sqrt {3}\right ) x^2} \, dx,x,\frac {1+\frac {2 \left (1-\sqrt {3}\right ) x}{-2+2 \sqrt {3}}}{\sqrt {-1+x^3}}\right )+\frac {1}{6} \left (6+\sqrt {3}\right ) \text {Subst}\left (\int \frac {1}{1-\left (3+2 \sqrt {3}\right ) x^2} \, dx,x,\frac {1+\frac {2 \left (1+\sqrt {3}\right ) x}{-2-2 \sqrt {3}}}{\sqrt {-1+x^3}}\right ) \\ & = \frac {1}{6} \sqrt {15+14 \sqrt {3}} \arctan \left (\frac {\sqrt {-3+2 \sqrt {3}} (1-x)}{\sqrt {-1+x^3}}\right )+\frac {1}{6} \sqrt {-15+14 \sqrt {3}} \text {arctanh}\left (\frac {\sqrt {3+2 \sqrt {3}} (1-x)}{\sqrt {-1+x^3}}\right )+\frac {\sqrt {38-21 \sqrt {3}} (1-x) \sqrt {\frac {1+x+x^2}{\left (1-\sqrt {3}-x\right )^2}} \operatorname {EllipticF}\left (\arcsin \left (\frac {1+\sqrt {3}-x}{1-\sqrt {3}-x}\right ),-7+4 \sqrt {3}\right )}{2\ 3^{3/4} \sqrt {-\frac {1-x}{\left (1-\sqrt {3}-x\right )^2}} \sqrt {-1+x^3}}+\frac {\sqrt {14-5 \sqrt {3}} (1-x) \sqrt {\frac {1+x+x^2}{\left (1-\sqrt {3}-x\right )^2}} \operatorname {EllipticF}\left (\arcsin \left (\frac {1+\sqrt {3}-x}{1-\sqrt {3}-x}\right ),-7+4 \sqrt {3}\right )}{2\ 3^{3/4} \sqrt {-\frac {1-x}{\left (1-\sqrt {3}-x\right )^2}} \sqrt {-1+x^3}}-\frac {2 \sqrt {2-\sqrt {3}} (1-x) \sqrt {\frac {1+x+x^2}{\left (1-\sqrt {3}-x\right )^2}} \operatorname {EllipticF}\left (\arcsin \left (\frac {1+\sqrt {3}-x}{1-\sqrt {3}-x}\right ),-7+4 \sqrt {3}\right )}{\sqrt [4]{3} \sqrt {-\frac {1-x}{\left (1-\sqrt {3}-x\right )^2}} \sqrt {-1+x^3}} \\ \end{align*}
Time = 1.59 (sec) , antiderivative size = 99, normalized size of antiderivative = 1.00 \[ \int \frac {3-x+x^2}{\left (-2-2 x+x^2\right ) \sqrt {-1+x^3}} \, dx=-\frac {1}{6} \sqrt {15+14 \sqrt {3}} \arctan \left (\frac {\sqrt {-3+2 \sqrt {3}} \sqrt {-1+x^3}}{1+x+x^2}\right )-\frac {1}{6} \sqrt {-15+14 \sqrt {3}} \text {arctanh}\left (\frac {\sqrt {3+2 \sqrt {3}} \sqrt {-1+x^3}}{1+x+x^2}\right ) \]
[In]
[Out]
Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 10.03 (sec) , antiderivative size = 591, normalized size of antiderivative = 5.97
method | result | size |
trager | \(-\frac {\operatorname {RootOf}\left (432 \textit {\_Z}^{4}+360 \textit {\_Z}^{2}-121\right ) \ln \left (\frac {-3888 \operatorname {RootOf}\left (432 \textit {\_Z}^{4}+360 \textit {\_Z}^{2}-121\right )^{5} x^{2}-7776 \operatorname {RootOf}\left (432 \textit {\_Z}^{4}+360 \textit {\_Z}^{2}-121\right )^{5} x +1800 \operatorname {RootOf}\left (432 \textit {\_Z}^{4}+360 \textit {\_Z}^{2}-121\right )^{3} x^{2}-2448 \operatorname {RootOf}\left (432 \textit {\_Z}^{4}+360 \textit {\_Z}^{2}-121\right )^{3} x +7392 \sqrt {x^{3}-1}\, \operatorname {RootOf}\left (432 \textit {\_Z}^{4}+360 \textit {\_Z}^{2}-121\right )^{2}+6048 \operatorname {RootOf}\left (432 \textit {\_Z}^{4}+360 \textit {\_Z}^{2}-121\right )^{3}+53 \operatorname {RootOf}\left (432 \textit {\_Z}^{4}+360 \textit {\_Z}^{2}-121\right ) x^{2}+3074 \operatorname {RootOf}\left (432 \textit {\_Z}^{4}+360 \textit {\_Z}^{2}-121\right ) x -1232 \sqrt {x^{3}-1}-2968 \operatorname {RootOf}\left (432 \textit {\_Z}^{4}+360 \textit {\_Z}^{2}-121\right )}{{\left (36 \operatorname {RootOf}\left (432 \textit {\_Z}^{4}+360 \textit {\_Z}^{2}-121\right )^{2} x +x -28\right )}^{2}}\right )}{2}+\frac {\operatorname {RootOf}\left (\textit {\_Z}^{2}+36 \operatorname {RootOf}\left (432 \textit {\_Z}^{4}+360 \textit {\_Z}^{2}-121\right )^{2}+30\right ) \ln \left (\frac {3888 \operatorname {RootOf}\left (\textit {\_Z}^{2}+36 \operatorname {RootOf}\left (432 \textit {\_Z}^{4}+360 \textit {\_Z}^{2}-121\right )^{2}+30\right ) \operatorname {RootOf}\left (432 \textit {\_Z}^{4}+360 \textit {\_Z}^{2}-121\right )^{4} x^{2}+7776 \operatorname {RootOf}\left (432 \textit {\_Z}^{4}+360 \textit {\_Z}^{2}-121\right )^{4} x \operatorname {RootOf}\left (\textit {\_Z}^{2}+36 \operatorname {RootOf}\left (432 \textit {\_Z}^{4}+360 \textit {\_Z}^{2}-121\right )^{2}+30\right )+8280 \operatorname {RootOf}\left (432 \textit {\_Z}^{4}+360 \textit {\_Z}^{2}-121\right )^{2} \operatorname {RootOf}\left (\textit {\_Z}^{2}+36 \operatorname {RootOf}\left (432 \textit {\_Z}^{4}+360 \textit {\_Z}^{2}-121\right )^{2}+30\right ) x^{2}+10512 \operatorname {RootOf}\left (432 \textit {\_Z}^{4}+360 \textit {\_Z}^{2}-121\right )^{2} \operatorname {RootOf}\left (\textit {\_Z}^{2}+36 \operatorname {RootOf}\left (432 \textit {\_Z}^{4}+360 \textit {\_Z}^{2}-121\right )^{2}+30\right ) x +6048 \operatorname {RootOf}\left (432 \textit {\_Z}^{4}+360 \textit {\_Z}^{2}-121\right )^{2} \operatorname {RootOf}\left (\textit {\_Z}^{2}+36 \operatorname {RootOf}\left (432 \textit {\_Z}^{4}+360 \textit {\_Z}^{2}-121\right )^{2}+30\right )+4147 \operatorname {RootOf}\left (\textit {\_Z}^{2}+36 \operatorname {RootOf}\left (432 \textit {\_Z}^{4}+360 \textit {\_Z}^{2}-121\right )^{2}+30\right ) x^{2}-44352 \sqrt {x^{3}-1}\, \operatorname {RootOf}\left (432 \textit {\_Z}^{4}+360 \textit {\_Z}^{2}-121\right )^{2}+286 \operatorname {RootOf}\left (\textit {\_Z}^{2}+36 \operatorname {RootOf}\left (432 \textit {\_Z}^{4}+360 \textit {\_Z}^{2}-121\right )^{2}+30\right ) x +8008 \operatorname {RootOf}\left (\textit {\_Z}^{2}+36 \operatorname {RootOf}\left (432 \textit {\_Z}^{4}+360 \textit {\_Z}^{2}-121\right )^{2}+30\right )-44352 \sqrt {x^{3}-1}}{{\left (36 \operatorname {RootOf}\left (432 \textit {\_Z}^{4}+360 \textit {\_Z}^{2}-121\right )^{2} x +29 x +28\right )}^{2}}\right )}{12}\) | \(591\) |
default | \(\text {Expression too large to display}\) | \(1517\) |
elliptic | \(\text {Expression too large to display}\) | \(1726\) |
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 403 vs. \(2 (75) = 150\).
Time = 0.30 (sec) , antiderivative size = 403, normalized size of antiderivative = 4.07 \[ \int \frac {3-x+x^2}{\left (-2-2 x+x^2\right ) \sqrt {-1+x^3}} \, dx=-\frac {1}{24} \, \sqrt {14 \, \sqrt {3} - 15} \log \left (\frac {11 \, x^{4} + 22 \, x^{3} + 66 \, x^{2} + 2 \, \sqrt {x^{3} - 1} {\left (4 \, x^{2} + \sqrt {3} {\left (3 \, x^{2} + 2 \, x + 4\right )} + 10 \, x - 2\right )} \sqrt {14 \, \sqrt {3} - 15} + 44 \, \sqrt {3} {\left (x^{3} - 1\right )} - 44 \, x + 44}{x^{4} - 4 \, x^{3} + 8 \, x + 4}\right ) + \frac {1}{24} \, \sqrt {14 \, \sqrt {3} - 15} \log \left (\frac {11 \, x^{4} + 22 \, x^{3} + 66 \, x^{2} - 2 \, \sqrt {x^{3} - 1} {\left (4 \, x^{2} + \sqrt {3} {\left (3 \, x^{2} + 2 \, x + 4\right )} + 10 \, x - 2\right )} \sqrt {14 \, \sqrt {3} - 15} + 44 \, \sqrt {3} {\left (x^{3} - 1\right )} - 44 \, x + 44}{x^{4} - 4 \, x^{3} + 8 \, x + 4}\right ) - \frac {1}{24} \, \sqrt {-14 \, \sqrt {3} - 15} \log \left (\frac {11 \, x^{4} + 22 \, x^{3} + 66 \, x^{2} + 2 \, \sqrt {x^{3} - 1} {\left (4 \, x^{2} - \sqrt {3} {\left (3 \, x^{2} + 2 \, x + 4\right )} + 10 \, x - 2\right )} \sqrt {-14 \, \sqrt {3} - 15} - 44 \, \sqrt {3} {\left (x^{3} - 1\right )} - 44 \, x + 44}{x^{4} - 4 \, x^{3} + 8 \, x + 4}\right ) + \frac {1}{24} \, \sqrt {-14 \, \sqrt {3} - 15} \log \left (\frac {11 \, x^{4} + 22 \, x^{3} + 66 \, x^{2} - 2 \, \sqrt {x^{3} - 1} {\left (4 \, x^{2} - \sqrt {3} {\left (3 \, x^{2} + 2 \, x + 4\right )} + 10 \, x - 2\right )} \sqrt {-14 \, \sqrt {3} - 15} - 44 \, \sqrt {3} {\left (x^{3} - 1\right )} - 44 \, x + 44}{x^{4} - 4 \, x^{3} + 8 \, x + 4}\right ) \]
[In]
[Out]
\[ \int \frac {3-x+x^2}{\left (-2-2 x+x^2\right ) \sqrt {-1+x^3}} \, dx=\int \frac {x^{2} - x + 3}{\sqrt {\left (x - 1\right ) \left (x^{2} + x + 1\right )} \left (x^{2} - 2 x - 2\right )}\, dx \]
[In]
[Out]
\[ \int \frac {3-x+x^2}{\left (-2-2 x+x^2\right ) \sqrt {-1+x^3}} \, dx=\int { \frac {x^{2} - x + 3}{\sqrt {x^{3} - 1} {\left (x^{2} - 2 \, x - 2\right )}} \,d x } \]
[In]
[Out]
\[ \int \frac {3-x+x^2}{\left (-2-2 x+x^2\right ) \sqrt {-1+x^3}} \, dx=\int { \frac {x^{2} - x + 3}{\sqrt {x^{3} - 1} {\left (x^{2} - 2 \, x - 2\right )}} \,d x } \]
[In]
[Out]
Time = 6.22 (sec) , antiderivative size = 505, normalized size of antiderivative = 5.10 \[ \int \frac {3-x+x^2}{\left (-2-2 x+x^2\right ) \sqrt {-1+x^3}} \, dx=-\frac {2\,\left (\frac {3}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}\right )\,\sqrt {-\frac {x+\frac {1}{2}-\frac {\sqrt {3}\,1{}\mathrm {i}}{2}}{-\frac {3}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}}}\,\sqrt {\frac {x+\frac {1}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}}{\frac {3}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}}}\,\sqrt {-\frac {x-1}{\frac {3}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}}}\,\mathrm {F}\left (\mathrm {asin}\left (\sqrt {-\frac {x-1}{\frac {3}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}}}\right )\middle |-\frac {\frac {3}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}}{-\frac {3}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}}\right )}{\sqrt {x^3+\left (-\left (-\frac {1}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}\right )\,\left (\frac {1}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}\right )-1\right )\,x+\left (-\frac {1}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}\right )\,\left (\frac {1}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}\right )}}-\frac {\left (\frac {3}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}\right )\,\sqrt {-\frac {x+\frac {1}{2}-\frac {\sqrt {3}\,1{}\mathrm {i}}{2}}{-\frac {3}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}}}\,\sqrt {\frac {x+\frac {1}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}}{\frac {3}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}}}\,\sqrt {-\frac {x-1}{\frac {3}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}}}\,\left (\sqrt {3}-6\right )\,\Pi \left (\frac {\sqrt {3}\,\left (\frac {3}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}\right )}{3};\mathrm {asin}\left (\sqrt {-\frac {x-1}{\frac {3}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}}}\right )\middle |-\frac {\frac {3}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}}{-\frac {3}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}}\right )}{3\,\sqrt {x^3+\left (-\left (-\frac {1}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}\right )\,\left (\frac {1}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}\right )-1\right )\,x+\left (-\frac {1}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}\right )\,\left (\frac {1}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}\right )}}+\frac {\left (\frac {3}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}\right )\,\sqrt {-\frac {x+\frac {1}{2}-\frac {\sqrt {3}\,1{}\mathrm {i}}{2}}{-\frac {3}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}}}\,\sqrt {\frac {x+\frac {1}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}}{\frac {3}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}}}\,\sqrt {-\frac {x-1}{\frac {3}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}}}\,\left (\sqrt {3}+6\right )\,\Pi \left (-\frac {\sqrt {3}\,\left (\frac {3}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}\right )}{3};\mathrm {asin}\left (\sqrt {-\frac {x-1}{\frac {3}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}}}\right )\middle |-\frac {\frac {3}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}}{-\frac {3}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}}\right )}{3\,\sqrt {x^3+\left (-\left (-\frac {1}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}\right )\,\left (\frac {1}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}\right )-1\right )\,x+\left (-\frac {1}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}\right )\,\left (\frac {1}{2}+\frac {\sqrt {3}\,1{}\mathrm {i}}{2}\right )}} \]
[In]
[Out]