3.552 \(\int \frac {(a+b x^2)^{5/2} (A+B x^2)}{x^9} \, dx\)

Optimal. Leaf size=152 \[ \frac {5 b^3 (A b-8 a B) \tanh ^{-1}\left (\frac {\sqrt {a+b x^2}}{\sqrt {a}}\right )}{128 a^{3/2}}+\frac {5 b^2 \sqrt {a+b x^2} (A b-8 a B)}{128 a x^2}+\frac {\left (a+b x^2\right )^{5/2} (A b-8 a B)}{48 a x^6}+\frac {5 b \left (a+b x^2\right )^{3/2} (A b-8 a B)}{192 a x^4}-\frac {A \left (a+b x^2\right )^{7/2}}{8 a x^8} \]

[Out]

5/192*b*(A*b-8*B*a)*(b*x^2+a)^(3/2)/a/x^4+1/48*(A*b-8*B*a)*(b*x^2+a)^(5/2)/a/x^6-1/8*A*(b*x^2+a)^(7/2)/a/x^8+5
/128*b^3*(A*b-8*B*a)*arctanh((b*x^2+a)^(1/2)/a^(1/2))/a^(3/2)+5/128*b^2*(A*b-8*B*a)*(b*x^2+a)^(1/2)/a/x^2

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Rubi [A]  time = 0.12, antiderivative size = 152, normalized size of antiderivative = 1.00, number of steps used = 7, number of rules used = 5, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.227, Rules used = {446, 78, 47, 63, 208} \[ \frac {5 b^3 (A b-8 a B) \tanh ^{-1}\left (\frac {\sqrt {a+b x^2}}{\sqrt {a}}\right )}{128 a^{3/2}}+\frac {5 b^2 \sqrt {a+b x^2} (A b-8 a B)}{128 a x^2}+\frac {\left (a+b x^2\right )^{5/2} (A b-8 a B)}{48 a x^6}+\frac {5 b \left (a+b x^2\right )^{3/2} (A b-8 a B)}{192 a x^4}-\frac {A \left (a+b x^2\right )^{7/2}}{8 a x^8} \]

Antiderivative was successfully verified.

[In]

Int[((a + b*x^2)^(5/2)*(A + B*x^2))/x^9,x]

[Out]

(5*b^2*(A*b - 8*a*B)*Sqrt[a + b*x^2])/(128*a*x^2) + (5*b*(A*b - 8*a*B)*(a + b*x^2)^(3/2))/(192*a*x^4) + ((A*b
- 8*a*B)*(a + b*x^2)^(5/2))/(48*a*x^6) - (A*(a + b*x^2)^(7/2))/(8*a*x^8) + (5*b^3*(A*b - 8*a*B)*ArcTanh[Sqrt[a
+ b*x^2]/Sqrt[a]])/(128*a^(3/2))

Rule 47

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> Simp[((a + b*x)^(m + 1)*(c + d*x)^n)/(b*
(m + 1)), x] - Dist[(d*n)/(b*(m + 1)), Int[(a + b*x)^(m + 1)*(c + d*x)^(n - 1), x], x] /; FreeQ[{a, b, c, d},
x] && NeQ[b*c - a*d, 0] && GtQ[n, 0] && LtQ[m, -1] &&  !(IntegerQ[n] &&  !IntegerQ[m]) &&  !(ILeQ[m + n + 2, 0
] && (FractionQ[m] || GeQ[2*n + m + 1, 0])) && IntLinearQ[a, b, c, d, m, n, x]

Rule 63

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> With[{p = Denominator[m]}, Dist[p/b, Sub
st[Int[x^(p*(m + 1) - 1)*(c - (a*d)/b + (d*x^p)/b)^n, x], x, (a + b*x)^(1/p)], x]] /; FreeQ[{a, b, c, d}, x] &
& NeQ[b*c - a*d, 0] && LtQ[-1, m, 0] && LeQ[-1, n, 0] && LeQ[Denominator[n], Denominator[m]] && IntLinearQ[a,
b, c, d, m, n, x]

Rule 78

Int[((a_.) + (b_.)*(x_))*((c_.) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> -Simp[((b*e - a*f
)*(c + d*x)^(n + 1)*(e + f*x)^(p + 1))/(f*(p + 1)*(c*f - d*e)), x] - Dist[(a*d*f*(n + p + 2) - b*(d*e*(n + 1)
+ c*f*(p + 1)))/(f*(p + 1)*(c*f - d*e)), Int[(c + d*x)^n*(e + f*x)^(p + 1), x], x] /; FreeQ[{a, b, c, d, e, f,
n}, x] && LtQ[p, -1] && ( !LtQ[n, -1] || IntegerQ[p] ||  !(IntegerQ[n] ||  !(EqQ[e, 0] ||  !(EqQ[c, 0] || LtQ
[p, n]))))

Rule 208

Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(Rt[-(a/b), 2]*ArcTanh[x/Rt[-(a/b), 2]])/a, x] /; FreeQ[{a,
b}, x] && NegQ[a/b]

Rule 446

Int[(x_)^(m_.)*((a_) + (b_.)*(x_)^(n_))^(p_.)*((c_) + (d_.)*(x_)^(n_))^(q_.), x_Symbol] :> Dist[1/n, Subst[Int
[x^(Simplify[(m + 1)/n] - 1)*(a + b*x)^p*(c + d*x)^q, x], x, x^n], x] /; FreeQ[{a, b, c, d, m, n, p, q}, x] &&
NeQ[b*c - a*d, 0] && IntegerQ[Simplify[(m + 1)/n]]

Rubi steps

\begin {align*} \int \frac {\left (a+b x^2\right )^{5/2} \left (A+B x^2\right )}{x^9} \, dx &=\frac {1}{2} \operatorname {Subst}\left (\int \frac {(a+b x)^{5/2} (A+B x)}{x^5} \, dx,x,x^2\right )\\ &=-\frac {A \left (a+b x^2\right )^{7/2}}{8 a x^8}+\frac {\left (-\frac {A b}{2}+4 a B\right ) \operatorname {Subst}\left (\int \frac {(a+b x)^{5/2}}{x^4} \, dx,x,x^2\right )}{8 a}\\ &=\frac {(A b-8 a B) \left (a+b x^2\right )^{5/2}}{48 a x^6}-\frac {A \left (a+b x^2\right )^{7/2}}{8 a x^8}-\frac {(5 b (A b-8 a B)) \operatorname {Subst}\left (\int \frac {(a+b x)^{3/2}}{x^3} \, dx,x,x^2\right )}{96 a}\\ &=\frac {5 b (A b-8 a B) \left (a+b x^2\right )^{3/2}}{192 a x^4}+\frac {(A b-8 a B) \left (a+b x^2\right )^{5/2}}{48 a x^6}-\frac {A \left (a+b x^2\right )^{7/2}}{8 a x^8}-\frac {\left (5 b^2 (A b-8 a B)\right ) \operatorname {Subst}\left (\int \frac {\sqrt {a+b x}}{x^2} \, dx,x,x^2\right )}{128 a}\\ &=\frac {5 b^2 (A b-8 a B) \sqrt {a+b x^2}}{128 a x^2}+\frac {5 b (A b-8 a B) \left (a+b x^2\right )^{3/2}}{192 a x^4}+\frac {(A b-8 a B) \left (a+b x^2\right )^{5/2}}{48 a x^6}-\frac {A \left (a+b x^2\right )^{7/2}}{8 a x^8}-\frac {\left (5 b^3 (A b-8 a B)\right ) \operatorname {Subst}\left (\int \frac {1}{x \sqrt {a+b x}} \, dx,x,x^2\right )}{256 a}\\ &=\frac {5 b^2 (A b-8 a B) \sqrt {a+b x^2}}{128 a x^2}+\frac {5 b (A b-8 a B) \left (a+b x^2\right )^{3/2}}{192 a x^4}+\frac {(A b-8 a B) \left (a+b x^2\right )^{5/2}}{48 a x^6}-\frac {A \left (a+b x^2\right )^{7/2}}{8 a x^8}-\frac {\left (5 b^2 (A b-8 a B)\right ) \operatorname {Subst}\left (\int \frac {1}{-\frac {a}{b}+\frac {x^2}{b}} \, dx,x,\sqrt {a+b x^2}\right )}{128 a}\\ &=\frac {5 b^2 (A b-8 a B) \sqrt {a+b x^2}}{128 a x^2}+\frac {5 b (A b-8 a B) \left (a+b x^2\right )^{3/2}}{192 a x^4}+\frac {(A b-8 a B) \left (a+b x^2\right )^{5/2}}{48 a x^6}-\frac {A \left (a+b x^2\right )^{7/2}}{8 a x^8}+\frac {5 b^3 (A b-8 a B) \tanh ^{-1}\left (\frac {\sqrt {a+b x^2}}{\sqrt {a}}\right )}{128 a^{3/2}}\\ \end {align*}

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Mathematica [A]  time = 0.14, size = 140, normalized size = 0.92 \[ \frac {-\left (a+b x^2\right ) \left (16 a^3 \left (3 A+4 B x^2\right )+8 a^2 b x^2 \left (17 A+26 B x^2\right )+2 a b^2 x^4 \left (59 A+132 B x^2\right )+15 A b^3 x^6\right )-15 b^3 x^8 \sqrt {\frac {b x^2}{a}+1} (8 a B-A b) \tanh ^{-1}\left (\sqrt {\frac {b x^2}{a}+1}\right )}{384 a x^8 \sqrt {a+b x^2}} \]

Antiderivative was successfully verified.

[In]

Integrate[((a + b*x^2)^(5/2)*(A + B*x^2))/x^9,x]

[Out]

(-((a + b*x^2)*(15*A*b^3*x^6 + 16*a^3*(3*A + 4*B*x^2) + 8*a^2*b*x^2*(17*A + 26*B*x^2) + 2*a*b^2*x^4*(59*A + 13
2*B*x^2))) - 15*b^3*(-(A*b) + 8*a*B)*x^8*Sqrt[1 + (b*x^2)/a]*ArcTanh[Sqrt[1 + (b*x^2)/a]])/(384*a*x^8*Sqrt[a +
b*x^2])

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fricas [A]  time = 0.78, size = 272, normalized size = 1.79 \[ \left [-\frac {15 \, {\left (8 \, B a b^{3} - A b^{4}\right )} \sqrt {a} x^{8} \log \left (-\frac {b x^{2} + 2 \, \sqrt {b x^{2} + a} \sqrt {a} + 2 \, a}{x^{2}}\right ) + 2 \, {\left (3 \, {\left (88 \, B a^{2} b^{2} + 5 \, A a b^{3}\right )} x^{6} + 48 \, A a^{4} + 2 \, {\left (104 \, B a^{3} b + 59 \, A a^{2} b^{2}\right )} x^{4} + 8 \, {\left (8 \, B a^{4} + 17 \, A a^{3} b\right )} x^{2}\right )} \sqrt {b x^{2} + a}}{768 \, a^{2} x^{8}}, \frac {15 \, {\left (8 \, B a b^{3} - A b^{4}\right )} \sqrt {-a} x^{8} \arctan \left (\frac {\sqrt {-a}}{\sqrt {b x^{2} + a}}\right ) - {\left (3 \, {\left (88 \, B a^{2} b^{2} + 5 \, A a b^{3}\right )} x^{6} + 48 \, A a^{4} + 2 \, {\left (104 \, B a^{3} b + 59 \, A a^{2} b^{2}\right )} x^{4} + 8 \, {\left (8 \, B a^{4} + 17 \, A a^{3} b\right )} x^{2}\right )} \sqrt {b x^{2} + a}}{384 \, a^{2} x^{8}}\right ] \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x^2+a)^(5/2)*(B*x^2+A)/x^9,x, algorithm="fricas")

[Out]

[-1/768*(15*(8*B*a*b^3 - A*b^4)*sqrt(a)*x^8*log(-(b*x^2 + 2*sqrt(b*x^2 + a)*sqrt(a) + 2*a)/x^2) + 2*(3*(88*B*a
^2*b^2 + 5*A*a*b^3)*x^6 + 48*A*a^4 + 2*(104*B*a^3*b + 59*A*a^2*b^2)*x^4 + 8*(8*B*a^4 + 17*A*a^3*b)*x^2)*sqrt(b
*x^2 + a))/(a^2*x^8), 1/384*(15*(8*B*a*b^3 - A*b^4)*sqrt(-a)*x^8*arctan(sqrt(-a)/sqrt(b*x^2 + a)) - (3*(88*B*a
^2*b^2 + 5*A*a*b^3)*x^6 + 48*A*a^4 + 2*(104*B*a^3*b + 59*A*a^2*b^2)*x^4 + 8*(8*B*a^4 + 17*A*a^3*b)*x^2)*sqrt(b
*x^2 + a))/(a^2*x^8)]

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giac [A]  time = 0.44, size = 195, normalized size = 1.28 \[ \frac {\frac {15 \, {\left (8 \, B a b^{4} - A b^{5}\right )} \arctan \left (\frac {\sqrt {b x^{2} + a}}{\sqrt {-a}}\right )}{\sqrt {-a} a} - \frac {264 \, {\left (b x^{2} + a\right )}^{\frac {7}{2}} B a b^{4} - 584 \, {\left (b x^{2} + a\right )}^{\frac {5}{2}} B a^{2} b^{4} + 440 \, {\left (b x^{2} + a\right )}^{\frac {3}{2}} B a^{3} b^{4} - 120 \, \sqrt {b x^{2} + a} B a^{4} b^{4} + 15 \, {\left (b x^{2} + a\right )}^{\frac {7}{2}} A b^{5} + 73 \, {\left (b x^{2} + a\right )}^{\frac {5}{2}} A a b^{5} - 55 \, {\left (b x^{2} + a\right )}^{\frac {3}{2}} A a^{2} b^{5} + 15 \, \sqrt {b x^{2} + a} A a^{3} b^{5}}{a b^{4} x^{8}}}{384 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x^2+a)^(5/2)*(B*x^2+A)/x^9,x, algorithm="giac")

[Out]

1/384*(15*(8*B*a*b^4 - A*b^5)*arctan(sqrt(b*x^2 + a)/sqrt(-a))/(sqrt(-a)*a) - (264*(b*x^2 + a)^(7/2)*B*a*b^4 -
584*(b*x^2 + a)^(5/2)*B*a^2*b^4 + 440*(b*x^2 + a)^(3/2)*B*a^3*b^4 - 120*sqrt(b*x^2 + a)*B*a^4*b^4 + 15*(b*x^2
+ a)^(7/2)*A*b^5 + 73*(b*x^2 + a)^(5/2)*A*a*b^5 - 55*(b*x^2 + a)^(3/2)*A*a^2*b^5 + 15*sqrt(b*x^2 + a)*A*a^3*b
^5)/(a*b^4*x^8))/b

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maple [B]  time = 0.02, size = 311, normalized size = 2.05 \[ \frac {5 A \,b^{4} \ln \left (\frac {2 a +2 \sqrt {b \,x^{2}+a}\, \sqrt {a}}{x}\right )}{128 a^{\frac {3}{2}}}-\frac {5 B \,b^{3} \ln \left (\frac {2 a +2 \sqrt {b \,x^{2}+a}\, \sqrt {a}}{x}\right )}{16 \sqrt {a}}-\frac {5 \sqrt {b \,x^{2}+a}\, A \,b^{4}}{128 a^{2}}+\frac {5 \sqrt {b \,x^{2}+a}\, B \,b^{3}}{16 a}-\frac {5 \left (b \,x^{2}+a \right )^{\frac {3}{2}} A \,b^{4}}{384 a^{3}}+\frac {5 \left (b \,x^{2}+a \right )^{\frac {3}{2}} B \,b^{3}}{48 a^{2}}-\frac {\left (b \,x^{2}+a \right )^{\frac {5}{2}} A \,b^{4}}{128 a^{4}}+\frac {\left (b \,x^{2}+a \right )^{\frac {5}{2}} B \,b^{3}}{16 a^{3}}+\frac {\left (b \,x^{2}+a \right )^{\frac {7}{2}} A \,b^{3}}{128 a^{4} x^{2}}-\frac {\left (b \,x^{2}+a \right )^{\frac {7}{2}} B \,b^{2}}{16 a^{3} x^{2}}+\frac {\left (b \,x^{2}+a \right )^{\frac {7}{2}} A \,b^{2}}{192 a^{3} x^{4}}-\frac {\left (b \,x^{2}+a \right )^{\frac {7}{2}} B b}{24 a^{2} x^{4}}+\frac {\left (b \,x^{2}+a \right )^{\frac {7}{2}} A b}{48 a^{2} x^{6}}-\frac {\left (b \,x^{2}+a \right )^{\frac {7}{2}} B}{6 a \,x^{6}}-\frac {\left (b \,x^{2}+a \right )^{\frac {7}{2}} A}{8 a \,x^{8}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((b*x^2+a)^(5/2)*(B*x^2+A)/x^9,x)

[Out]

-1/6*B/a/x^6*(b*x^2+a)^(7/2)-1/24*B*b/a^2/x^4*(b*x^2+a)^(7/2)-1/16*B*b^2/a^3/x^2*(b*x^2+a)^(7/2)+1/16*B*b^3/a^
3*(b*x^2+a)^(5/2)+5/48*B*b^3/a^2*(b*x^2+a)^(3/2)-5/16*B*b^3/a^(1/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)+5/16
*B*b^3/a*(b*x^2+a)^(1/2)-1/8*A*(b*x^2+a)^(7/2)/a/x^8+1/48*A*b/a^2/x^6*(b*x^2+a)^(7/2)+1/192*A*b^2/a^3/x^4*(b*x
^2+a)^(7/2)+1/128*A*b^3/a^4/x^2*(b*x^2+a)^(7/2)-1/128*A*b^4/a^4*(b*x^2+a)^(5/2)-5/384*A*b^4/a^3*(b*x^2+a)^(3/2
)+5/128*A*b^4/a^(3/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)-5/128*A*b^4/a^2*(b*x^2+a)^(1/2)

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maxima [B]  time = 1.17, size = 288, normalized size = 1.89 \[ -\frac {5 \, B b^{3} \operatorname {arsinh}\left (\frac {a}{\sqrt {a b} {\left | x \right |}}\right )}{16 \, \sqrt {a}} + \frac {5 \, A b^{4} \operatorname {arsinh}\left (\frac {a}{\sqrt {a b} {\left | x \right |}}\right )}{128 \, a^{\frac {3}{2}}} + \frac {{\left (b x^{2} + a\right )}^{\frac {5}{2}} B b^{3}}{16 \, a^{3}} + \frac {5 \, {\left (b x^{2} + a\right )}^{\frac {3}{2}} B b^{3}}{48 \, a^{2}} + \frac {5 \, \sqrt {b x^{2} + a} B b^{3}}{16 \, a} - \frac {{\left (b x^{2} + a\right )}^{\frac {5}{2}} A b^{4}}{128 \, a^{4}} - \frac {5 \, {\left (b x^{2} + a\right )}^{\frac {3}{2}} A b^{4}}{384 \, a^{3}} - \frac {5 \, \sqrt {b x^{2} + a} A b^{4}}{128 \, a^{2}} - \frac {{\left (b x^{2} + a\right )}^{\frac {7}{2}} B b^{2}}{16 \, a^{3} x^{2}} + \frac {{\left (b x^{2} + a\right )}^{\frac {7}{2}} A b^{3}}{128 \, a^{4} x^{2}} - \frac {{\left (b x^{2} + a\right )}^{\frac {7}{2}} B b}{24 \, a^{2} x^{4}} + \frac {{\left (b x^{2} + a\right )}^{\frac {7}{2}} A b^{2}}{192 \, a^{3} x^{4}} - \frac {{\left (b x^{2} + a\right )}^{\frac {7}{2}} B}{6 \, a x^{6}} + \frac {{\left (b x^{2} + a\right )}^{\frac {7}{2}} A b}{48 \, a^{2} x^{6}} - \frac {{\left (b x^{2} + a\right )}^{\frac {7}{2}} A}{8 \, a x^{8}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x^2+a)^(5/2)*(B*x^2+A)/x^9,x, algorithm="maxima")

[Out]

-5/16*B*b^3*arcsinh(a/(sqrt(a*b)*abs(x)))/sqrt(a) + 5/128*A*b^4*arcsinh(a/(sqrt(a*b)*abs(x)))/a^(3/2) + 1/16*(
b*x^2 + a)^(5/2)*B*b^3/a^3 + 5/48*(b*x^2 + a)^(3/2)*B*b^3/a^2 + 5/16*sqrt(b*x^2 + a)*B*b^3/a - 1/128*(b*x^2 +
a)^(5/2)*A*b^4/a^4 - 5/384*(b*x^2 + a)^(3/2)*A*b^4/a^3 - 5/128*sqrt(b*x^2 + a)*A*b^4/a^2 - 1/16*(b*x^2 + a)^(7
/2)*B*b^2/(a^3*x^2) + 1/128*(b*x^2 + a)^(7/2)*A*b^3/(a^4*x^2) - 1/24*(b*x^2 + a)^(7/2)*B*b/(a^2*x^4) + 1/192*(
b*x^2 + a)^(7/2)*A*b^2/(a^3*x^4) - 1/6*(b*x^2 + a)^(7/2)*B/(a*x^6) + 1/48*(b*x^2 + a)^(7/2)*A*b/(a^2*x^6) - 1/
8*(b*x^2 + a)^(7/2)*A/(a*x^8)

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mupad [B]  time = 4.58, size = 169, normalized size = 1.11 \[ \frac {55\,A\,a\,{\left (b\,x^2+a\right )}^{3/2}}{384\,x^8}-\frac {11\,B\,{\left (b\,x^2+a\right )}^{5/2}}{16\,x^6}-\frac {73\,A\,{\left (b\,x^2+a\right )}^{5/2}}{384\,x^8}+\frac {5\,B\,a\,{\left (b\,x^2+a\right )}^{3/2}}{6\,x^6}-\frac {5\,A\,a^2\,\sqrt {b\,x^2+a}}{128\,x^8}-\frac {5\,A\,{\left (b\,x^2+a\right )}^{7/2}}{128\,a\,x^8}-\frac {5\,B\,a^2\,\sqrt {b\,x^2+a}}{16\,x^6}-\frac {A\,b^4\,\mathrm {atan}\left (\frac {\sqrt {b\,x^2+a}\,1{}\mathrm {i}}{\sqrt {a}}\right )\,5{}\mathrm {i}}{128\,a^{3/2}}+\frac {B\,b^3\,\mathrm {atan}\left (\frac {\sqrt {b\,x^2+a}\,1{}\mathrm {i}}{\sqrt {a}}\right )\,5{}\mathrm {i}}{16\,\sqrt {a}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((A + B*x^2)*(a + b*x^2)^(5/2))/x^9,x)

[Out]

(B*b^3*atan(((a + b*x^2)^(1/2)*1i)/a^(1/2))*5i)/(16*a^(1/2)) - (11*B*(a + b*x^2)^(5/2))/(16*x^6) - (A*b^4*atan
(((a + b*x^2)^(1/2)*1i)/a^(1/2))*5i)/(128*a^(3/2)) - (73*A*(a + b*x^2)^(5/2))/(384*x^8) + (55*A*a*(a + b*x^2)^
(3/2))/(384*x^8) + (5*B*a*(a + b*x^2)^(3/2))/(6*x^6) - (5*A*a^2*(a + b*x^2)^(1/2))/(128*x^8) - (5*A*(a + b*x^2
)^(7/2))/(128*a*x^8) - (5*B*a^2*(a + b*x^2)^(1/2))/(16*x^6)

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((b*x**2+a)**(5/2)*(B*x**2+A)/x**9,x)

[Out]

Timed out

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