Optimal. Leaf size=51 \[ 2 \tanh ^{-1}\left (\frac {x^2-1}{\sqrt [4]{\frac {x+1}{x^2-2}}}\right )-2 \tan ^{-1}\left (\frac {\sqrt [4]{\frac {x+1}{x^2-2}}}{x^2-1}\right ) \]
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Rubi [F] time = 9.30, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {2+16 x-x^2-9 x^3}{\sqrt [4]{\frac {1+x}{-2+x^2}} \left (-2+x^2\right ) \left (-3+2 x+7 x^2-7 x^3-9 x^4+9 x^5+5 x^6-5 x^7-x^8+x^9\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {2+16 x-x^2-9 x^3}{\sqrt [4]{\frac {1+x}{-2+x^2}} \left (-2+x^2\right ) \left (-3+2 x+7 x^2-7 x^3-9 x^4+9 x^5+5 x^6-5 x^7-x^8+x^9\right )} \, dx &=\int \frac {\left (\frac {1+x}{-2+x^2}\right )^{3/4} \left (-2-16 x+x^2+9 x^3\right )}{3+x-9 x^2+16 x^4-14 x^6+6 x^8-x^{10}} \, dx\\ &=\frac {\left (\left (\frac {1+x}{-2+x^2}\right )^{3/4} \left (-2+x^2\right )^{3/4}\right ) \int \frac {(1+x)^{3/4} \left (-2-16 x+x^2+9 x^3\right )}{\left (-2+x^2\right )^{3/4} \left (3+x-9 x^2+16 x^4-14 x^6+6 x^8-x^{10}\right )} \, dx}{(1+x)^{3/4}}\\ &=\frac {\left (\left (\frac {1+x}{-2+x^2}\right )^{3/4} \left (-2+x^2\right )^{3/4}\right ) \int \frac {-2-16 x+x^2+9 x^3}{\sqrt [4]{1+x} \left (-2+x^2\right )^{3/4} \left (3-2 x-7 x^2+7 x^3+9 x^4-9 x^5-5 x^6+5 x^7+x^8-x^9\right )} \, dx}{(1+x)^{3/4}}\\ &=\frac {\left (\left (\frac {1+x}{-2+x^2}\right )^{3/4} \left (-2+x^2\right )^{3/4}\right ) \int \left (\frac {2}{\sqrt [4]{1+x} \left (-2+x^2\right )^{3/4} \left (-3+2 x+7 x^2-7 x^3-9 x^4+9 x^5+5 x^6-5 x^7-x^8+x^9\right )}+\frac {16 x}{\sqrt [4]{1+x} \left (-2+x^2\right )^{3/4} \left (-3+2 x+7 x^2-7 x^3-9 x^4+9 x^5+5 x^6-5 x^7-x^8+x^9\right )}-\frac {x^2}{\sqrt [4]{1+x} \left (-2+x^2\right )^{3/4} \left (-3+2 x+7 x^2-7 x^3-9 x^4+9 x^5+5 x^6-5 x^7-x^8+x^9\right )}-\frac {9 x^3}{\sqrt [4]{1+x} \left (-2+x^2\right )^{3/4} \left (-3+2 x+7 x^2-7 x^3-9 x^4+9 x^5+5 x^6-5 x^7-x^8+x^9\right )}\right ) \, dx}{(1+x)^{3/4}}\\ &=-\frac {\left (\left (\frac {1+x}{-2+x^2}\right )^{3/4} \left (-2+x^2\right )^{3/4}\right ) \int \frac {x^2}{\sqrt [4]{1+x} \left (-2+x^2\right )^{3/4} \left (-3+2 x+7 x^2-7 x^3-9 x^4+9 x^5+5 x^6-5 x^7-x^8+x^9\right )} \, dx}{(1+x)^{3/4}}+\frac {\left (2 \left (\frac {1+x}{-2+x^2}\right )^{3/4} \left (-2+x^2\right )^{3/4}\right ) \int \frac {1}{\sqrt [4]{1+x} \left (-2+x^2\right )^{3/4} \left (-3+2 x+7 x^2-7 x^3-9 x^4+9 x^5+5 x^6-5 x^7-x^8+x^9\right )} \, dx}{(1+x)^{3/4}}-\frac {\left (9 \left (\frac {1+x}{-2+x^2}\right )^{3/4} \left (-2+x^2\right )^{3/4}\right ) \int \frac {x^3}{\sqrt [4]{1+x} \left (-2+x^2\right )^{3/4} \left (-3+2 x+7 x^2-7 x^3-9 x^4+9 x^5+5 x^6-5 x^7-x^8+x^9\right )} \, dx}{(1+x)^{3/4}}+\frac {\left (16 \left (\frac {1+x}{-2+x^2}\right )^{3/4} \left (-2+x^2\right )^{3/4}\right ) \int \frac {x}{\sqrt [4]{1+x} \left (-2+x^2\right )^{3/4} \left (-3+2 x+7 x^2-7 x^3-9 x^4+9 x^5+5 x^6-5 x^7-x^8+x^9\right )} \, dx}{(1+x)^{3/4}}\\ &=-\frac {\left (4 \left (\frac {1+x}{-2+x^2}\right )^{3/4} \left (-2+x^2\right )^{3/4}\right ) \operatorname {Subst}\left (\int \frac {x^2 \left (-1+x^4\right )^2}{\left (-1-2 x^4+x^8\right )^{3/4} \left (-1-16 x^{12}+56 x^{20}-72 x^{24}+39 x^{28}-10 x^{32}+x^{36}\right )} \, dx,x,\sqrt [4]{1+x}\right )}{(1+x)^{3/4}}+\frac {\left (8 \left (\frac {1+x}{-2+x^2}\right )^{3/4} \left (-2+x^2\right )^{3/4}\right ) \operatorname {Subst}\left (\int \frac {x^2}{\left (-1-2 x^4+x^8\right )^{3/4} \left (-1-16 x^{12}+56 x^{20}-72 x^{24}+39 x^{28}-10 x^{32}+x^{36}\right )} \, dx,x,\sqrt [4]{1+x}\right )}{(1+x)^{3/4}}-\frac {\left (36 \left (\frac {1+x}{-2+x^2}\right )^{3/4} \left (-2+x^2\right )^{3/4}\right ) \operatorname {Subst}\left (\int \frac {x^2 \left (-1+x^4\right )^3}{\left (-1-2 x^4+x^8\right )^{3/4} \left (-1-16 x^{12}+56 x^{20}-72 x^{24}+39 x^{28}-10 x^{32}+x^{36}\right )} \, dx,x,\sqrt [4]{1+x}\right )}{(1+x)^{3/4}}+\frac {\left (64 \left (\frac {1+x}{-2+x^2}\right )^{3/4} \left (-2+x^2\right )^{3/4}\right ) \operatorname {Subst}\left (\int \frac {x^2 \left (-1+x^4\right )}{\left (-1-2 x^4+x^8\right )^{3/4} \left (-1-16 x^{12}+56 x^{20}-72 x^{24}+39 x^{28}-10 x^{32}+x^{36}\right )} \, dx,x,\sqrt [4]{1+x}\right )}{(1+x)^{3/4}}\\ &=-\frac {\left (4 \left (\frac {1+x}{-2+x^2}\right )^{3/4} \left (-2+x^2\right )^{3/4}\right ) \operatorname {Subst}\left (\int \left (\frac {x^2}{\left (-1-2 x^4+x^8\right )^{3/4} \left (-1-16 x^{12}+56 x^{20}-72 x^{24}+39 x^{28}-10 x^{32}+x^{36}\right )}-\frac {2 x^6}{\left (-1-2 x^4+x^8\right )^{3/4} \left (-1-16 x^{12}+56 x^{20}-72 x^{24}+39 x^{28}-10 x^{32}+x^{36}\right )}+\frac {x^{10}}{\left (-1-2 x^4+x^8\right )^{3/4} \left (-1-16 x^{12}+56 x^{20}-72 x^{24}+39 x^{28}-10 x^{32}+x^{36}\right )}\right ) \, dx,x,\sqrt [4]{1+x}\right )}{(1+x)^{3/4}}+\frac {\left (8 \left (\frac {1+x}{-2+x^2}\right )^{3/4} \left (-2+x^2\right )^{3/4}\right ) \operatorname {Subst}\left (\int \frac {x^2}{\left (-1-2 x^4+x^8\right )^{3/4} \left (-1-16 x^{12}+56 x^{20}-72 x^{24}+39 x^{28}-10 x^{32}+x^{36}\right )} \, dx,x,\sqrt [4]{1+x}\right )}{(1+x)^{3/4}}-\frac {\left (36 \left (\frac {1+x}{-2+x^2}\right )^{3/4} \left (-2+x^2\right )^{3/4}\right ) \operatorname {Subst}\left (\int \left (-\frac {x^2}{\left (-1-2 x^4+x^8\right )^{3/4} \left (-1-16 x^{12}+56 x^{20}-72 x^{24}+39 x^{28}-10 x^{32}+x^{36}\right )}+\frac {3 x^6}{\left (-1-2 x^4+x^8\right )^{3/4} \left (-1-16 x^{12}+56 x^{20}-72 x^{24}+39 x^{28}-10 x^{32}+x^{36}\right )}-\frac {3 x^{10}}{\left (-1-2 x^4+x^8\right )^{3/4} \left (-1-16 x^{12}+56 x^{20}-72 x^{24}+39 x^{28}-10 x^{32}+x^{36}\right )}+\frac {x^{14}}{\left (-1-2 x^4+x^8\right )^{3/4} \left (-1-16 x^{12}+56 x^{20}-72 x^{24}+39 x^{28}-10 x^{32}+x^{36}\right )}\right ) \, dx,x,\sqrt [4]{1+x}\right )}{(1+x)^{3/4}}+\frac {\left (64 \left (\frac {1+x}{-2+x^2}\right )^{3/4} \left (-2+x^2\right )^{3/4}\right ) \operatorname {Subst}\left (\int \left (-\frac {x^2}{\left (-1-2 x^4+x^8\right )^{3/4} \left (-1-16 x^{12}+56 x^{20}-72 x^{24}+39 x^{28}-10 x^{32}+x^{36}\right )}+\frac {x^6}{\left (-1-2 x^4+x^8\right )^{3/4} \left (-1-16 x^{12}+56 x^{20}-72 x^{24}+39 x^{28}-10 x^{32}+x^{36}\right )}\right ) \, dx,x,\sqrt [4]{1+x}\right )}{(1+x)^{3/4}}\\ &=-\frac {\left (4 \left (\frac {1+x}{-2+x^2}\right )^{3/4} \left (-2+x^2\right )^{3/4}\right ) \operatorname {Subst}\left (\int \frac {x^2}{\left (-1-2 x^4+x^8\right )^{3/4} \left (-1-16 x^{12}+56 x^{20}-72 x^{24}+39 x^{28}-10 x^{32}+x^{36}\right )} \, dx,x,\sqrt [4]{1+x}\right )}{(1+x)^{3/4}}-\frac {\left (4 \left (\frac {1+x}{-2+x^2}\right )^{3/4} \left (-2+x^2\right )^{3/4}\right ) \operatorname {Subst}\left (\int \frac {x^{10}}{\left (-1-2 x^4+x^8\right )^{3/4} \left (-1-16 x^{12}+56 x^{20}-72 x^{24}+39 x^{28}-10 x^{32}+x^{36}\right )} \, dx,x,\sqrt [4]{1+x}\right )}{(1+x)^{3/4}}+\frac {\left (8 \left (\frac {1+x}{-2+x^2}\right )^{3/4} \left (-2+x^2\right )^{3/4}\right ) \operatorname {Subst}\left (\int \frac {x^2}{\left (-1-2 x^4+x^8\right )^{3/4} \left (-1-16 x^{12}+56 x^{20}-72 x^{24}+39 x^{28}-10 x^{32}+x^{36}\right )} \, dx,x,\sqrt [4]{1+x}\right )}{(1+x)^{3/4}}+\frac {\left (8 \left (\frac {1+x}{-2+x^2}\right )^{3/4} \left (-2+x^2\right )^{3/4}\right ) \operatorname {Subst}\left (\int \frac {x^6}{\left (-1-2 x^4+x^8\right )^{3/4} \left (-1-16 x^{12}+56 x^{20}-72 x^{24}+39 x^{28}-10 x^{32}+x^{36}\right )} \, dx,x,\sqrt [4]{1+x}\right )}{(1+x)^{3/4}}+\frac {\left (36 \left (\frac {1+x}{-2+x^2}\right )^{3/4} \left (-2+x^2\right )^{3/4}\right ) \operatorname {Subst}\left (\int \frac {x^2}{\left (-1-2 x^4+x^8\right )^{3/4} \left (-1-16 x^{12}+56 x^{20}-72 x^{24}+39 x^{28}-10 x^{32}+x^{36}\right )} \, dx,x,\sqrt [4]{1+x}\right )}{(1+x)^{3/4}}-\frac {\left (36 \left (\frac {1+x}{-2+x^2}\right )^{3/4} \left (-2+x^2\right )^{3/4}\right ) \operatorname {Subst}\left (\int \frac {x^{14}}{\left (-1-2 x^4+x^8\right )^{3/4} \left (-1-16 x^{12}+56 x^{20}-72 x^{24}+39 x^{28}-10 x^{32}+x^{36}\right )} \, dx,x,\sqrt [4]{1+x}\right )}{(1+x)^{3/4}}-\frac {\left (64 \left (\frac {1+x}{-2+x^2}\right )^{3/4} \left (-2+x^2\right )^{3/4}\right ) \operatorname {Subst}\left (\int \frac {x^2}{\left (-1-2 x^4+x^8\right )^{3/4} \left (-1-16 x^{12}+56 x^{20}-72 x^{24}+39 x^{28}-10 x^{32}+x^{36}\right )} \, dx,x,\sqrt [4]{1+x}\right )}{(1+x)^{3/4}}+\frac {\left (64 \left (\frac {1+x}{-2+x^2}\right )^{3/4} \left (-2+x^2\right )^{3/4}\right ) \operatorname {Subst}\left (\int \frac {x^6}{\left (-1-2 x^4+x^8\right )^{3/4} \left (-1-16 x^{12}+56 x^{20}-72 x^{24}+39 x^{28}-10 x^{32}+x^{36}\right )} \, dx,x,\sqrt [4]{1+x}\right )}{(1+x)^{3/4}}-\frac {\left (108 \left (\frac {1+x}{-2+x^2}\right )^{3/4} \left (-2+x^2\right )^{3/4}\right ) \operatorname {Subst}\left (\int \frac {x^6}{\left (-1-2 x^4+x^8\right )^{3/4} \left (-1-16 x^{12}+56 x^{20}-72 x^{24}+39 x^{28}-10 x^{32}+x^{36}\right )} \, dx,x,\sqrt [4]{1+x}\right )}{(1+x)^{3/4}}+\frac {\left (108 \left (\frac {1+x}{-2+x^2}\right )^{3/4} \left (-2+x^2\right )^{3/4}\right ) \operatorname {Subst}\left (\int \frac {x^{10}}{\left (-1-2 x^4+x^8\right )^{3/4} \left (-1-16 x^{12}+56 x^{20}-72 x^{24}+39 x^{28}-10 x^{32}+x^{36}\right )} \, dx,x,\sqrt [4]{1+x}\right )}{(1+x)^{3/4}}\\ \end {align*}
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Mathematica [F] time = 2.08, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {2+16 x-x^2-9 x^3}{\sqrt [4]{\frac {1+x}{-2+x^2}} \left (-2+x^2\right ) \left (-3+2 x+7 x^2-7 x^3-9 x^4+9 x^5+5 x^6-5 x^7-x^8+x^9\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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IntegrateAlgebraic [A] time = 0.20, size = 51, normalized size = 1.00 \begin {gather*} -2 \tan ^{-1}\left (\frac {\sqrt [4]{\frac {1+x}{-2+x^2}}}{-1+x^2}\right )+2 \tanh ^{-1}\left (\frac {-1+x^2}{\sqrt [4]{\frac {1+x}{-2+x^2}}}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 100.27, size = 331, normalized size = 6.49 \begin {gather*} -\arctan \left (\frac {2 \, {\left ({\left (x^{3} - x^{2} - 2 \, x + 2\right )} \left (\frac {x + 1}{x^{2} - 2}\right )^{\frac {3}{4}} + {\left (x^{7} - x^{6} - 4 \, x^{5} + 4 \, x^{4} + 5 \, x^{3} - 5 \, x^{2} - 2 \, x + 2\right )} \left (\frac {x + 1}{x^{2} - 2}\right )^{\frac {1}{4}}\right )}}{x^{9} - x^{8} - 5 \, x^{7} + 5 \, x^{6} + 9 \, x^{5} - 9 \, x^{4} - 7 \, x^{3} + 7 \, x^{2} + 2 \, x - 3}\right ) + \log \left (-\frac {x^{9} - x^{8} - 5 \, x^{7} + 5 \, x^{6} + 9 \, x^{5} - 9 \, x^{4} - 7 \, x^{3} + 7 \, x^{2} + 2 \, {\left (x^{3} - x^{2} - 2 \, x + 2\right )} \left (\frac {x + 1}{x^{2} - 2}\right )^{\frac {3}{4}} + 2 \, {\left (x^{5} - x^{4} - 3 \, x^{3} + 3 \, x^{2} + 2 \, x - 2\right )} \sqrt {\frac {x + 1}{x^{2} - 2}} + 2 \, {\left (x^{7} - x^{6} - 4 \, x^{5} + 4 \, x^{4} + 5 \, x^{3} - 5 \, x^{2} - 2 \, x + 2\right )} \left (\frac {x + 1}{x^{2} - 2}\right )^{\frac {1}{4}} + 2 \, x - 1}{x^{9} - x^{8} - 5 \, x^{7} + 5 \, x^{6} + 9 \, x^{5} - 9 \, x^{4} - 7 \, x^{3} + 7 \, x^{2} + 2 \, x - 3}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {9 \, x^{3} + x^{2} - 16 \, x - 2}{{\left (x^{9} - x^{8} - 5 \, x^{7} + 5 \, x^{6} + 9 \, x^{5} - 9 \, x^{4} - 7 \, x^{3} + 7 \, x^{2} + 2 \, x - 3\right )} {\left (x^{2} - 2\right )} \left (\frac {x + 1}{x^{2} - 2}\right )^{\frac {1}{4}}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 13.18, size = 1012, normalized size = 19.84
method | result | size |
trager | \(\ln \left (-\frac {-1+2 x +x^{9}-5 x^{7}+9 x^{5}+5 x^{6}+7 x^{2}-7 x^{3}-x^{8}-9 x^{4}+4 \left (-\frac {-1-x}{x^{2}-2}\right )^{\frac {1}{4}}-4 \sqrt {-\frac {-1-x}{x^{2}-2}}+4 \left (-\frac {-1-x}{x^{2}-2}\right )^{\frac {3}{4}}+2 \sqrt {-\frac {-1-x}{x^{2}-2}}\, x^{5}-2 \sqrt {-\frac {-1-x}{x^{2}-2}}\, x^{4}-6 \sqrt {-\frac {-1-x}{x^{2}-2}}\, x^{3}+6 \sqrt {-\frac {-1-x}{x^{2}-2}}\, x^{2}+4 \sqrt {-\frac {-1-x}{x^{2}-2}}\, x +2 \left (-\frac {-1-x}{x^{2}-2}\right )^{\frac {1}{4}} x^{7}-2 \left (-\frac {-1-x}{x^{2}-2}\right )^{\frac {1}{4}} x^{6}+2 \left (-\frac {-1-x}{x^{2}-2}\right )^{\frac {3}{4}} x^{3}-8 \left (-\frac {-1-x}{x^{2}-2}\right )^{\frac {1}{4}} x^{5}-2 \left (-\frac {-1-x}{x^{2}-2}\right )^{\frac {3}{4}} x^{2}+8 \left (-\frac {-1-x}{x^{2}-2}\right )^{\frac {1}{4}} x^{4}-4 \left (-\frac {-1-x}{x^{2}-2}\right )^{\frac {3}{4}} x +10 \left (-\frac {-1-x}{x^{2}-2}\right )^{\frac {1}{4}} x^{3}-10 \left (-\frac {-1-x}{x^{2}-2}\right )^{\frac {1}{4}} x^{2}-4 \left (-\frac {-1-x}{x^{2}-2}\right )^{\frac {1}{4}} x}{x^{9}-x^{8}-5 x^{7}+5 x^{6}+9 x^{5}-9 x^{4}-7 x^{3}+7 x^{2}+2 x -3}\right )+\RootOf \left (\textit {\_Z}^{2}+1\right ) \ln \left (\frac {\RootOf \left (\textit {\_Z}^{2}+1\right )+4 \left (-\frac {-1-x}{x^{2}-2}\right )^{\frac {1}{4}}-4 \left (-\frac {-1-x}{x^{2}-2}\right )^{\frac {3}{4}}-2 \RootOf \left (\textit {\_Z}^{2}+1\right ) x -\RootOf \left (\textit {\_Z}^{2}+1\right ) x^{9}+\RootOf \left (\textit {\_Z}^{2}+1\right ) x^{8}+5 \RootOf \left (\textit {\_Z}^{2}+1\right ) x^{7}-9 \RootOf \left (\textit {\_Z}^{2}+1\right ) x^{5}+9 \RootOf \left (\textit {\_Z}^{2}+1\right ) x^{4}+7 \RootOf \left (\textit {\_Z}^{2}+1\right ) x^{3}-4 \sqrt {-\frac {-1-x}{x^{2}-2}}\, \RootOf \left (\textit {\_Z}^{2}+1\right )-5 \RootOf \left (\textit {\_Z}^{2}+1\right ) x^{6}-7 \RootOf \left (\textit {\_Z}^{2}+1\right ) x^{2}-6 \sqrt {-\frac {-1-x}{x^{2}-2}}\, \RootOf \left (\textit {\_Z}^{2}+1\right ) x^{3}+6 \sqrt {-\frac {-1-x}{x^{2}-2}}\, \RootOf \left (\textit {\_Z}^{2}+1\right ) x^{2}+4 \sqrt {-\frac {-1-x}{x^{2}-2}}\, \RootOf \left (\textit {\_Z}^{2}+1\right ) x +2 \sqrt {-\frac {-1-x}{x^{2}-2}}\, \RootOf \left (\textit {\_Z}^{2}+1\right ) x^{5}-2 \sqrt {-\frac {-1-x}{x^{2}-2}}\, \RootOf \left (\textit {\_Z}^{2}+1\right ) x^{4}+2 \left (-\frac {-1-x}{x^{2}-2}\right )^{\frac {1}{4}} x^{7}-2 \left (-\frac {-1-x}{x^{2}-2}\right )^{\frac {1}{4}} x^{6}-2 \left (-\frac {-1-x}{x^{2}-2}\right )^{\frac {3}{4}} x^{3}-8 \left (-\frac {-1-x}{x^{2}-2}\right )^{\frac {1}{4}} x^{5}+2 \left (-\frac {-1-x}{x^{2}-2}\right )^{\frac {3}{4}} x^{2}+8 \left (-\frac {-1-x}{x^{2}-2}\right )^{\frac {1}{4}} x^{4}+4 \left (-\frac {-1-x}{x^{2}-2}\right )^{\frac {3}{4}} x +10 \left (-\frac {-1-x}{x^{2}-2}\right )^{\frac {1}{4}} x^{3}-10 \left (-\frac {-1-x}{x^{2}-2}\right )^{\frac {1}{4}} x^{2}-4 \left (-\frac {-1-x}{x^{2}-2}\right )^{\frac {1}{4}} x}{x^{9}-x^{8}-5 x^{7}+5 x^{6}+9 x^{5}-9 x^{4}-7 x^{3}+7 x^{2}+2 x -3}\right )\) | \(1012\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} -\int \frac {9 \, x^{3} + x^{2} - 16 \, x - 2}{{\left (x^{9} - x^{8} - 5 \, x^{7} + 5 \, x^{6} + 9 \, x^{5} - 9 \, x^{4} - 7 \, x^{3} + 7 \, x^{2} + 2 \, x - 3\right )} {\left (x^{2} - 2\right )} \left (\frac {x + 1}{x^{2} - 2}\right )^{\frac {1}{4}}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.02 \begin {gather*} \int \frac {-9\,x^3-x^2+16\,x+2}{\left (x^2-2\right )\,{\left (\frac {x+1}{x^2-2}\right )}^{1/4}\,\left (x^9-x^8-5\,x^7+5\,x^6+9\,x^5-9\,x^4-7\,x^3+7\,x^2+2\,x-3\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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