3.28.60 \(\int \frac {x^5 (2 x^5 c_3-3 c_4) \sqrt {\frac {x^3 c_0+x^5 c_3+c_4}{x^3 c_1+x^5 c_3+c_4}}}{(x^3+2 x^5 c_3+2 c_4) (-x^6+x^{10} c_3{}^2+2 x^5 c_3 c_4+c_4{}^2)} \, dx\)

Optimal. Leaf size=259 \[ \frac {\sqrt {1-c_0} \tan ^{-1}\left (\frac {\sqrt {1-c_0} \sqrt {-1+c_1} \sqrt {\frac {c_3 x^5+c_0 x^3+c_4}{c_3 x^5+c_1 x^3+c_4}}}{-1+c_0}\right )}{\sqrt {-1+c_1}}+\frac {\sqrt {-1-c_0} \tan ^{-1}\left (\frac {\sqrt {-1-c_0} \sqrt {1+c_1} \sqrt {\frac {c_3 x^5+c_0 x^3+c_4}{c_3 x^5+c_1 x^3+c_4}}}{1+c_0}\right )}{3 \sqrt {1+c_1}}-\frac {4 \sqrt {1-2 c_0} \tan ^{-1}\left (\frac {\sqrt {1-2 c_0} \sqrt {-1+2 c_1} \sqrt {\frac {c_3 x^5+c_0 x^3+c_4}{c_3 x^5+c_1 x^3+c_4}}}{-1+2 c_0}\right )}{3 \sqrt {-1+2 c_1}} \]

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Rubi [F]  time = 41.72, 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 {x^5 \left (2 x^5 c_3-3 c_4\right ) \sqrt {\frac {x^3 c_0+x^5 c_3+c_4}{x^3 c_1+x^5 c_3+c_4}}}{\left (x^3+2 x^5 c_3+2 c_4\right ) \left (-x^6+x^{10} c_3{}^2+2 x^5 c_3 c_4+c_4{}^2\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(x^5*(2*x^5*C[3] - 3*C[4])*Sqrt[(x^3*C[0] + x^5*C[3] + C[4])/(x^3*C[1] + x^5*C[3] + C[4])])/((x^3 + 2*x^5*
C[3] + 2*C[4])*(-x^6 + x^10*C[3]^2 + 2*x^5*C[3]*C[4] + C[4]^2)),x]

[Out]

-1/2*(Sqrt[(x^3*C[0] + x^5*C[3] + C[4])/(x^3*C[1] + x^5*C[3] + C[4])]*Sqrt[x^3*C[1] + x^5*C[3] + C[4]]*Defer[I
nt][(x^2*Sqrt[x^3*C[0] + x^5*C[3] + C[4]])/((-x^3 + x^5*C[3] + C[4])*Sqrt[x^3*C[1] + x^5*C[3] + C[4]]), x])/Sq
rt[x^3*C[0] + x^5*C[3] + C[4]] + (5*C[3]*Sqrt[(x^3*C[0] + x^5*C[3] + C[4])/(x^3*C[1] + x^5*C[3] + C[4])]*Sqrt[
x^3*C[1] + x^5*C[3] + C[4]]*Defer[Int][(x^4*Sqrt[x^3*C[0] + x^5*C[3] + C[4]])/((-x^3 + x^5*C[3] + C[4])*Sqrt[x
^3*C[1] + x^5*C[3] + C[4]]), x])/(6*Sqrt[x^3*C[0] + x^5*C[3] + C[4]]) + (3*Sqrt[(x^3*C[0] + x^5*C[3] + C[4])/(
x^3*C[1] + x^5*C[3] + C[4])]*Sqrt[x^3*C[1] + x^5*C[3] + C[4]]*Defer[Int][(x^2*Sqrt[x^3*C[0] + x^5*C[3] + C[4]]
)/((x^3 + x^5*C[3] + C[4])*Sqrt[x^3*C[1] + x^5*C[3] + C[4]]), x])/(2*Sqrt[x^3*C[0] + x^5*C[3] + C[4]]) + (5*C[
3]*Sqrt[(x^3*C[0] + x^5*C[3] + C[4])/(x^3*C[1] + x^5*C[3] + C[4])]*Sqrt[x^3*C[1] + x^5*C[3] + C[4]]*Defer[Int]
[(x^4*Sqrt[x^3*C[0] + x^5*C[3] + C[4]])/((x^3 + x^5*C[3] + C[4])*Sqrt[x^3*C[1] + x^5*C[3] + C[4]]), x])/(2*Sqr
t[x^3*C[0] + x^5*C[3] + C[4]]) - (2*Sqrt[(x^3*C[0] + x^5*C[3] + C[4])/(x^3*C[1] + x^5*C[3] + C[4])]*Sqrt[x^3*C
[1] + x^5*C[3] + C[4]]*Defer[Int][(x^2*Sqrt[x^3*C[0] + x^5*C[3] + C[4]])/(Sqrt[x^3*C[1] + x^5*C[3] + C[4]]*(x^
3 + 2*x^5*C[3] + 2*C[4])), x])/Sqrt[x^3*C[0] + x^5*C[3] + C[4]] - (20*C[3]*Sqrt[(x^3*C[0] + x^5*C[3] + C[4])/(
x^3*C[1] + x^5*C[3] + C[4])]*Sqrt[x^3*C[1] + x^5*C[3] + C[4]]*Defer[Int][(x^4*Sqrt[x^3*C[0] + x^5*C[3] + C[4]]
)/(Sqrt[x^3*C[1] + x^5*C[3] + C[4]]*(x^3 + 2*x^5*C[3] + 2*C[4])), x])/(3*Sqrt[x^3*C[0] + x^5*C[3] + C[4]])

Rubi steps

\begin {align*} \int \frac {x^5 \left (2 x^5 c_3-3 c_4\right ) \sqrt {\frac {x^3 c_0+x^5 c_3+c_4}{x^3 c_1+x^5 c_3+c_4}}}{\left (x^3+2 x^5 c_3+2 c_4\right ) \left (-x^6+x^{10} c_3{}^2+2 x^5 c_3 c_4+c_4{}^2\right )} \, dx &=\frac {\left (\sqrt {\frac {x^3 c_0+x^5 c_3+c_4}{x^3 c_1+x^5 c_3+c_4}} \sqrt {x^3 c_1+x^5 c_3+c_4}\right ) \int \frac {x^5 \left (2 x^5 c_3-3 c_4\right ) \sqrt {x^3 c_0+x^5 c_3+c_4}}{\sqrt {x^3 c_1+x^5 c_3+c_4} \left (x^3+2 x^5 c_3+2 c_4\right ) \left (-x^6+x^{10} c_3{}^2+2 x^5 c_3 c_4+c_4{}^2\right )} \, dx}{\sqrt {x^3 c_0+x^5 c_3+c_4}}\\ &=\frac {\left (\sqrt {\frac {x^3 c_0+x^5 c_3+c_4}{x^3 c_1+x^5 c_3+c_4}} \sqrt {x^3 c_1+x^5 c_3+c_4}\right ) \int \left (\frac {x^2 \left (-3+5 x^2 c_3\right ) \sqrt {x^3 c_0+x^5 c_3+c_4}}{6 \left (-x^3+x^5 c_3+c_4\right ) \sqrt {x^3 c_1+x^5 c_3+c_4}}+\frac {x^2 \left (3+5 x^2 c_3\right ) \sqrt {x^3 c_0+x^5 c_3+c_4}}{2 \left (x^3+x^5 c_3+c_4\right ) \sqrt {x^3 c_1+x^5 c_3+c_4}}-\frac {2 x^2 \left (3+10 x^2 c_3\right ) \sqrt {x^3 c_0+x^5 c_3+c_4}}{3 \sqrt {x^3 c_1+x^5 c_3+c_4} \left (x^3+2 x^5 c_3+2 c_4\right )}\right ) \, dx}{\sqrt {x^3 c_0+x^5 c_3+c_4}}\\ &=\frac {\left (\sqrt {\frac {x^3 c_0+x^5 c_3+c_4}{x^3 c_1+x^5 c_3+c_4}} \sqrt {x^3 c_1+x^5 c_3+c_4}\right ) \int \frac {x^2 \left (-3+5 x^2 c_3\right ) \sqrt {x^3 c_0+x^5 c_3+c_4}}{\left (-x^3+x^5 c_3+c_4\right ) \sqrt {x^3 c_1+x^5 c_3+c_4}} \, dx}{6 \sqrt {x^3 c_0+x^5 c_3+c_4}}+\frac {\left (\sqrt {\frac {x^3 c_0+x^5 c_3+c_4}{x^3 c_1+x^5 c_3+c_4}} \sqrt {x^3 c_1+x^5 c_3+c_4}\right ) \int \frac {x^2 \left (3+5 x^2 c_3\right ) \sqrt {x^3 c_0+x^5 c_3+c_4}}{\left (x^3+x^5 c_3+c_4\right ) \sqrt {x^3 c_1+x^5 c_3+c_4}} \, dx}{2 \sqrt {x^3 c_0+x^5 c_3+c_4}}-\frac {\left (2 \sqrt {\frac {x^3 c_0+x^5 c_3+c_4}{x^3 c_1+x^5 c_3+c_4}} \sqrt {x^3 c_1+x^5 c_3+c_4}\right ) \int \frac {x^2 \left (3+10 x^2 c_3\right ) \sqrt {x^3 c_0+x^5 c_3+c_4}}{\sqrt {x^3 c_1+x^5 c_3+c_4} \left (x^3+2 x^5 c_3+2 c_4\right )} \, dx}{3 \sqrt {x^3 c_0+x^5 c_3+c_4}}\\ &=\frac {\left (\sqrt {\frac {x^3 c_0+x^5 c_3+c_4}{x^3 c_1+x^5 c_3+c_4}} \sqrt {x^3 c_1+x^5 c_3+c_4}\right ) \int \left (-\frac {3 x^2 \sqrt {x^3 c_0+x^5 c_3+c_4}}{\left (-x^3+x^5 c_3+c_4\right ) \sqrt {x^3 c_1+x^5 c_3+c_4}}+\frac {5 x^4 c_3 \sqrt {x^3 c_0+x^5 c_3+c_4}}{\left (-x^3+x^5 c_3+c_4\right ) \sqrt {x^3 c_1+x^5 c_3+c_4}}\right ) \, dx}{6 \sqrt {x^3 c_0+x^5 c_3+c_4}}+\frac {\left (\sqrt {\frac {x^3 c_0+x^5 c_3+c_4}{x^3 c_1+x^5 c_3+c_4}} \sqrt {x^3 c_1+x^5 c_3+c_4}\right ) \int \left (\frac {3 x^2 \sqrt {x^3 c_0+x^5 c_3+c_4}}{\left (x^3+x^5 c_3+c_4\right ) \sqrt {x^3 c_1+x^5 c_3+c_4}}+\frac {5 x^4 c_3 \sqrt {x^3 c_0+x^5 c_3+c_4}}{\left (x^3+x^5 c_3+c_4\right ) \sqrt {x^3 c_1+x^5 c_3+c_4}}\right ) \, dx}{2 \sqrt {x^3 c_0+x^5 c_3+c_4}}-\frac {\left (2 \sqrt {\frac {x^3 c_0+x^5 c_3+c_4}{x^3 c_1+x^5 c_3+c_4}} \sqrt {x^3 c_1+x^5 c_3+c_4}\right ) \int \left (\frac {3 x^2 \sqrt {x^3 c_0+x^5 c_3+c_4}}{\sqrt {x^3 c_1+x^5 c_3+c_4} \left (x^3+2 x^5 c_3+2 c_4\right )}+\frac {10 x^4 c_3 \sqrt {x^3 c_0+x^5 c_3+c_4}}{\sqrt {x^3 c_1+x^5 c_3+c_4} \left (x^3+2 x^5 c_3+2 c_4\right )}\right ) \, dx}{3 \sqrt {x^3 c_0+x^5 c_3+c_4}}\\ &=-\frac {\left (\sqrt {\frac {x^3 c_0+x^5 c_3+c_4}{x^3 c_1+x^5 c_3+c_4}} \sqrt {x^3 c_1+x^5 c_3+c_4}\right ) \int \frac {x^2 \sqrt {x^3 c_0+x^5 c_3+c_4}}{\left (-x^3+x^5 c_3+c_4\right ) \sqrt {x^3 c_1+x^5 c_3+c_4}} \, dx}{2 \sqrt {x^3 c_0+x^5 c_3+c_4}}+\frac {\left (3 \sqrt {\frac {x^3 c_0+x^5 c_3+c_4}{x^3 c_1+x^5 c_3+c_4}} \sqrt {x^3 c_1+x^5 c_3+c_4}\right ) \int \frac {x^2 \sqrt {x^3 c_0+x^5 c_3+c_4}}{\left (x^3+x^5 c_3+c_4\right ) \sqrt {x^3 c_1+x^5 c_3+c_4}} \, dx}{2 \sqrt {x^3 c_0+x^5 c_3+c_4}}-\frac {\left (2 \sqrt {\frac {x^3 c_0+x^5 c_3+c_4}{x^3 c_1+x^5 c_3+c_4}} \sqrt {x^3 c_1+x^5 c_3+c_4}\right ) \int \frac {x^2 \sqrt {x^3 c_0+x^5 c_3+c_4}}{\sqrt {x^3 c_1+x^5 c_3+c_4} \left (x^3+2 x^5 c_3+2 c_4\right )} \, dx}{\sqrt {x^3 c_0+x^5 c_3+c_4}}+\frac {\left (5 c_3 \sqrt {\frac {x^3 c_0+x^5 c_3+c_4}{x^3 c_1+x^5 c_3+c_4}} \sqrt {x^3 c_1+x^5 c_3+c_4}\right ) \int \frac {x^4 \sqrt {x^3 c_0+x^5 c_3+c_4}}{\left (-x^3+x^5 c_3+c_4\right ) \sqrt {x^3 c_1+x^5 c_3+c_4}} \, dx}{6 \sqrt {x^3 c_0+x^5 c_3+c_4}}+\frac {\left (5 c_3 \sqrt {\frac {x^3 c_0+x^5 c_3+c_4}{x^3 c_1+x^5 c_3+c_4}} \sqrt {x^3 c_1+x^5 c_3+c_4}\right ) \int \frac {x^4 \sqrt {x^3 c_0+x^5 c_3+c_4}}{\left (x^3+x^5 c_3+c_4\right ) \sqrt {x^3 c_1+x^5 c_3+c_4}} \, dx}{2 \sqrt {x^3 c_0+x^5 c_3+c_4}}-\frac {\left (20 c_3 \sqrt {\frac {x^3 c_0+x^5 c_3+c_4}{x^3 c_1+x^5 c_3+c_4}} \sqrt {x^3 c_1+x^5 c_3+c_4}\right ) \int \frac {x^4 \sqrt {x^3 c_0+x^5 c_3+c_4}}{\sqrt {x^3 c_1+x^5 c_3+c_4} \left (x^3+2 x^5 c_3+2 c_4\right )} \, dx}{3 \sqrt {x^3 c_0+x^5 c_3+c_4}}\\ \end {align*}

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Mathematica [F]  time = 0.64, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x^5 \left (2 x^5 c_3-3 c_4\right ) \sqrt {\frac {x^3 c_0+x^5 c_3+c_4}{x^3 c_1+x^5 c_3+c_4}}}{\left (x^3+2 x^5 c_3+2 c_4\right ) \left (-x^6+x^{10} c_3{}^2+2 x^5 c_3 c_4+c_4{}^2\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(x^5*(2*x^5*C[3] - 3*C[4])*Sqrt[(x^3*C[0] + x^5*C[3] + C[4])/(x^3*C[1] + x^5*C[3] + C[4])])/((x^3 +
2*x^5*C[3] + 2*C[4])*(-x^6 + x^10*C[3]^2 + 2*x^5*C[3]*C[4] + C[4]^2)),x]

[Out]

Integrate[(x^5*(2*x^5*C[3] - 3*C[4])*Sqrt[(x^3*C[0] + x^5*C[3] + C[4])/(x^3*C[1] + x^5*C[3] + C[4])])/((x^3 +
2*x^5*C[3] + 2*C[4])*(-x^6 + x^10*C[3]^2 + 2*x^5*C[3]*C[4] + C[4]^2)), x]

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IntegrateAlgebraic [A]  time = 1.94, size = 259, normalized size = 1.00 \begin {gather*} \frac {\tan ^{-1}\left (\frac {\sqrt {1-c_0} \sqrt {-1+c_1} \sqrt {\frac {x^3 c_0+x^5 c_3+c_4}{x^3 c_1+x^5 c_3+c_4}}}{-1+c_0}\right ) \sqrt {1-c_0}}{\sqrt {-1+c_1}}+\frac {\tan ^{-1}\left (\frac {\sqrt {-1-c_0} \sqrt {1+c_1} \sqrt {\frac {x^3 c_0+x^5 c_3+c_4}{x^3 c_1+x^5 c_3+c_4}}}{1+c_0}\right ) \sqrt {-1-c_0}}{3 \sqrt {1+c_1}}-\frac {4 \tan ^{-1}\left (\frac {\sqrt {1-2 c_0} \sqrt {-1+2 c_1} \sqrt {\frac {x^3 c_0+x^5 c_3+c_4}{x^3 c_1+x^5 c_3+c_4}}}{-1+2 c_0}\right ) \sqrt {1-2 c_0}}{3 \sqrt {-1+2 c_1}} \end {gather*}

Antiderivative was successfully verified.

[In]

IntegrateAlgebraic[(x^5*(2*x^5*C[3] - 3*C[4])*Sqrt[(x^3*C[0] + x^5*C[3] + C[4])/(x^3*C[1] + x^5*C[3] + C[4])])
/((x^3 + 2*x^5*C[3] + 2*C[4])*(-x^6 + x^10*C[3]^2 + 2*x^5*C[3]*C[4] + C[4]^2)),x]

[Out]

(ArcTan[(Sqrt[1 - C[0]]*Sqrt[-1 + C[1]]*Sqrt[(x^3*C[0] + x^5*C[3] + C[4])/(x^3*C[1] + x^5*C[3] + C[4])])/(-1 +
C[0])]*Sqrt[1 - C[0]])/Sqrt[-1 + C[1]] + (ArcTan[(Sqrt[-1 - C[0]]*Sqrt[1 + C[1]]*Sqrt[(x^3*C[0] + x^5*C[3] +
C[4])/(x^3*C[1] + x^5*C[3] + C[4])])/(1 + C[0])]*Sqrt[-1 - C[0]])/(3*Sqrt[1 + C[1]]) - (4*ArcTan[(Sqrt[1 - 2*C
[0]]*Sqrt[-1 + 2*C[1]]*Sqrt[(x^3*C[0] + x^5*C[3] + C[4])/(x^3*C[1] + x^5*C[3] + C[4])])/(-1 + 2*C[0])]*Sqrt[1
- 2*C[0]])/(3*Sqrt[-1 + 2*C[1]])

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fricas [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.

[In]

integrate(x^5*(2*_C3*x^5-3*_C4)*((_C3*x^5+_C0*x^3+_C4)/(_C3*x^5+_C1*x^3+_C4))^(1/2)/(2*_C3*x^5+x^3+2*_C4)/(_C3
^2*x^10+2*_C3*_C4*x^5-x^6+_C4^2),x, algorithm="fricas")

[Out]

Timed out

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giac [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.

[In]

integrate(x^5*(2*_C3*x^5-3*_C4)*((_C3*x^5+_C0*x^3+_C4)/(_C3*x^5+_C1*x^3+_C4))^(1/2)/(2*_C3*x^5+x^3+2*_C4)/(_C3
^2*x^10+2*_C3*_C4*x^5-x^6+_C4^2),x, algorithm="giac")

[Out]

Timed out

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maple [F]  time = 0.14, size = 0, normalized size = 0.00 \[\int \frac {x^{5} \left (2 \textit {\_C3} \,x^{5}-3 \textit {\_C4} \right ) \sqrt {\frac {\textit {\_C3} \,x^{5}+\textit {\_C0} \,x^{3}+\textit {\_C4}}{\textit {\_C3} \,x^{5}+\textit {\_C1} \,x^{3}+\textit {\_C4}}}}{\left (2 \textit {\_C3} \,x^{5}+x^{3}+2 \textit {\_C4} \right ) \left (\textit {\_C3}^{2} x^{10}+2 \textit {\_C3} \textit {\_C4} \,x^{5}-x^{6}+\textit {\_C4}^{2}\right )}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^5*(2*_C3*x^5-3*_C4)*((_C3*x^5+_C0*x^3+_C4)/(_C3*x^5+_C1*x^3+_C4))^(1/2)/(2*_C3*x^5+x^3+2*_C4)/(_C3^2*x^1
0+2*_C3*_C4*x^5-x^6+_C4^2),x)

[Out]

int(x^5*(2*_C3*x^5-3*_C4)*((_C3*x^5+_C0*x^3+_C4)/(_C3*x^5+_C1*x^3+_C4))^(1/2)/(2*_C3*x^5+x^3+2*_C4)/(_C3^2*x^1
0+2*_C3*_C4*x^5-x^6+_C4^2),x)

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (2 \, \_{C_{3}} x^{5} - 3 \, \_{C_{4}}\right )} x^{5} \sqrt {\frac {\_{C_{3}} x^{5} + \_{C_{0}} x^{3} + \_{C_{4}}}{\_{C_{3}} x^{5} + \_{C_{1}} x^{3} + \_{C_{4}}}}}{{\left (\_{C_{3}}^{2} x^{10} + 2 \, \_{C_{3}} \_{C_{4}} x^{5} - x^{6} + \_{C_{4}}^{2}\right )} {\left (2 \, \_{C_{3}} x^{5} + x^{3} + 2 \, \_{C_{4}}\right )}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^5*(2*_C3*x^5-3*_C4)*((_C3*x^5+_C0*x^3+_C4)/(_C3*x^5+_C1*x^3+_C4))^(1/2)/(2*_C3*x^5+x^3+2*_C4)/(_C3
^2*x^10+2*_C3*_C4*x^5-x^6+_C4^2),x, algorithm="maxima")

[Out]

integrate((2*_C3*x^5 - 3*_C4)*x^5*sqrt((_C3*x^5 + _C0*x^3 + _C4)/(_C3*x^5 + _C1*x^3 + _C4))/((_C3^2*x^10 + 2*_
C3*_C4*x^5 - x^6 + _C4^2)*(2*_C3*x^5 + x^3 + 2*_C4)), x)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.00 \begin {gather*} \int -\frac {x^5\,\sqrt {\frac {_{\mathrm {C3}}\,x^5+_{\mathrm {C0}}\,x^3+_{\mathrm {C4}}}{_{\mathrm {C3}}\,x^5+_{\mathrm {C1}}\,x^3+_{\mathrm {C4}}}}\,\left (3\,_{\mathrm {C4}}-2\,_{\mathrm {C3}}\,x^5\right )}{\left (2\,_{\mathrm {C3}}\,x^5+x^3+2\,_{\mathrm {C4}}\right )\,\left ({_{\mathrm {C3}}}^2\,x^{10}+2\,_{\mathrm {C3}}\,_{\mathrm {C4}}\,x^5+{_{\mathrm {C4}}}^2-x^6\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(x^5*((_C4 + _C0*x^3 + _C3*x^5)/(_C4 + _C1*x^3 + _C3*x^5))^(1/2)*(3*_C4 - 2*_C3*x^5))/((2*_C4 + 2*_C3*x^5
+ x^3)*(_C4^2 - x^6 + _C3^2*x^10 + 2*_C3*_C4*x^5)),x)

[Out]

int(-(x^5*((_C4 + _C0*x^3 + _C3*x^5)/(_C4 + _C1*x^3 + _C3*x^5))^(1/2)*(3*_C4 - 2*_C3*x^5))/((2*_C4 + 2*_C3*x^5
+ x^3)*(_C4^2 - x^6 + _C3^2*x^10 + 2*_C3*_C4*x^5)), x)

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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.

[In]

integrate(x**5*(2*_C3*x**5-3*_C4)*((_C3*x**5+_C0*x**3+_C4)/(_C3*x**5+_C1*x**3+_C4))**(1/2)/(2*_C3*x**5+x**3+2*
_C4)/(_C3**2*x**10+2*_C3*_C4*x**5-x**6+_C4**2),x)

[Out]

Timed out

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