3.336 \(\int \frac{(3-x+2 x^2)^{3/2} (2+x+3 x^2-x^3+5 x^4)}{5+2 x} \, dx\)

Optimal. Leaf size=172 \[ \frac{5}{112} (2 x+5)^2 \left (2 x^2-x+3\right )^{5/2}-\frac{311}{448} (2 x+5) \left (2 x^2-x+3\right )^{5/2}+\frac{3505}{896} \left (2 x^2-x+3\right )^{5/2}+\frac{(500141-123060 x) \left (2 x^2-x+3\right )^{3/2}}{12288}+\frac{(141051019-23482924 x) \sqrt{2 x^2-x+3}}{65536}-\frac{99009 \tanh ^{-1}\left (\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right )}{8 \sqrt{2}}+\frac{1622009981 \sinh ^{-1}\left (\frac{1-4 x}{\sqrt{23}}\right )}{131072 \sqrt{2}} \]

[Out]

((141051019 - 23482924*x)*Sqrt[3 - x + 2*x^2])/65536 + ((500141 - 123060*x)*(3 - x + 2*x^2)^(3/2))/12288 + (35
05*(3 - x + 2*x^2)^(5/2))/896 - (311*(5 + 2*x)*(3 - x + 2*x^2)^(5/2))/448 + (5*(5 + 2*x)^2*(3 - x + 2*x^2)^(5/
2))/112 + (1622009981*ArcSinh[(1 - 4*x)/Sqrt[23]])/(131072*Sqrt[2]) - (99009*ArcTanh[(17 - 22*x)/(12*Sqrt[2]*S
qrt[3 - x + 2*x^2])])/(8*Sqrt[2])

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Rubi [A]  time = 0.268163, antiderivative size = 172, normalized size of antiderivative = 1., number of steps used = 10, number of rules used = 7, integrand size = 40, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.175, Rules used = {1653, 814, 843, 619, 215, 724, 206} \[ \frac{5}{112} (2 x+5)^2 \left (2 x^2-x+3\right )^{5/2}-\frac{311}{448} (2 x+5) \left (2 x^2-x+3\right )^{5/2}+\frac{3505}{896} \left (2 x^2-x+3\right )^{5/2}+\frac{(500141-123060 x) \left (2 x^2-x+3\right )^{3/2}}{12288}+\frac{(141051019-23482924 x) \sqrt{2 x^2-x+3}}{65536}-\frac{99009 \tanh ^{-1}\left (\frac{17-22 x}{12 \sqrt{2} \sqrt{2 x^2-x+3}}\right )}{8 \sqrt{2}}+\frac{1622009981 \sinh ^{-1}\left (\frac{1-4 x}{\sqrt{23}}\right )}{131072 \sqrt{2}} \]

Antiderivative was successfully verified.

[In]

Int[((3 - x + 2*x^2)^(3/2)*(2 + x + 3*x^2 - x^3 + 5*x^4))/(5 + 2*x),x]

[Out]

((141051019 - 23482924*x)*Sqrt[3 - x + 2*x^2])/65536 + ((500141 - 123060*x)*(3 - x + 2*x^2)^(3/2))/12288 + (35
05*(3 - x + 2*x^2)^(5/2))/896 - (311*(5 + 2*x)*(3 - x + 2*x^2)^(5/2))/448 + (5*(5 + 2*x)^2*(3 - x + 2*x^2)^(5/
2))/112 + (1622009981*ArcSinh[(1 - 4*x)/Sqrt[23]])/(131072*Sqrt[2]) - (99009*ArcTanh[(17 - 22*x)/(12*Sqrt[2]*S
qrt[3 - x + 2*x^2])])/(8*Sqrt[2])

Rule 1653

Int[(Pq_)*((d_.) + (e_.)*(x_))^(m_.)*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> With[{q = Expon[Pq
, x], f = Coeff[Pq, x, Expon[Pq, x]]}, Simp[(f*(d + e*x)^(m + q - 1)*(a + b*x + c*x^2)^(p + 1))/(c*e^(q - 1)*(
m + q + 2*p + 1)), x] + Dist[1/(c*e^q*(m + q + 2*p + 1)), Int[(d + e*x)^m*(a + b*x + c*x^2)^p*ExpandToSum[c*e^
q*(m + q + 2*p + 1)*Pq - c*f*(m + q + 2*p + 1)*(d + e*x)^q - f*(d + e*x)^(q - 2)*(b*d*e*(p + 1) + a*e^2*(m + q
- 1) - c*d^2*(m + q + 2*p + 1) - e*(2*c*d - b*e)*(m + q + p)*x), x], x], x] /; GtQ[q, 1] && NeQ[m + q + 2*p +
1, 0]] /; FreeQ[{a, b, c, d, e, m, p}, x] && PolyQ[Pq, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[c*d^2 - b*d*e + a*e^2
, 0] &&  !(IGtQ[m, 0] && RationalQ[a, b, c, d, e] && (IntegerQ[p] || ILtQ[p + 1/2, 0]))

Rule 814

Int[((d_.) + (e_.)*(x_))^(m_)*((f_.) + (g_.)*(x_))*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :> Sim
p[((d + e*x)^(m + 1)*(c*e*f*(m + 2*p + 2) - g*(c*d + 2*c*d*p - b*e*p) + g*c*e*(m + 2*p + 1)*x)*(a + b*x + c*x^
2)^p)/(c*e^2*(m + 2*p + 1)*(m + 2*p + 2)), x] - Dist[p/(c*e^2*(m + 2*p + 1)*(m + 2*p + 2)), Int[(d + e*x)^m*(a
+ b*x + c*x^2)^(p - 1)*Simp[c*e*f*(b*d - 2*a*e)*(m + 2*p + 2) + g*(a*e*(b*e - 2*c*d*m + b*e*m) + b*d*(b*e*p -
c*d - 2*c*d*p)) + (c*e*f*(2*c*d - b*e)*(m + 2*p + 2) + g*(b^2*e^2*(p + m + 1) - 2*c^2*d^2*(1 + 2*p) - c*e*(b*
d*(m - 2*p) + 2*a*e*(m + 2*p + 1))))*x, x], x], x] /; FreeQ[{a, b, c, d, e, f, g, m}, x] && NeQ[b^2 - 4*a*c, 0
] && NeQ[c*d^2 - b*d*e + a*e^2, 0] && GtQ[p, 0] && (IntegerQ[p] ||  !RationalQ[m] || (GeQ[m, -1] && LtQ[m, 0])
) &&  !ILtQ[m + 2*p, 0] && (IntegerQ[m] || IntegerQ[p] || IntegersQ[2*m, 2*p])

Rule 843

Int[((d_.) + (e_.)*(x_))^(m_)*((f_.) + (g_.)*(x_))*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :> Dis
t[g/e, Int[(d + e*x)^(m + 1)*(a + b*x + c*x^2)^p, x], x] + Dist[(e*f - d*g)/e, Int[(d + e*x)^m*(a + b*x + c*x^
2)^p, x], x] /; FreeQ[{a, b, c, d, e, f, g, m, p}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[c*d^2 - b*d*e + a*e^2, 0]
&&  !IGtQ[m, 0]

Rule 619

Int[((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> Dist[1/(2*c*((-4*c)/(b^2 - 4*a*c))^p), Subst[Int[Si
mp[1 - x^2/(b^2 - 4*a*c), x]^p, x], x, b + 2*c*x], x] /; FreeQ[{a, b, c, p}, x] && GtQ[4*a - b^2/c, 0]

Rule 215

Int[1/Sqrt[(a_) + (b_.)*(x_)^2], x_Symbol] :> Simp[ArcSinh[(Rt[b, 2]*x)/Sqrt[a]]/Rt[b, 2], x] /; FreeQ[{a, b},
x] && GtQ[a, 0] && PosQ[b]

Rule 724

Int[1/(((d_.) + (e_.)*(x_))*Sqrt[(a_.) + (b_.)*(x_) + (c_.)*(x_)^2]), x_Symbol] :> Dist[-2, Subst[Int[1/(4*c*d
^2 - 4*b*d*e + 4*a*e^2 - x^2), x], x, (2*a*e - b*d - (2*c*d - b*e)*x)/Sqrt[a + b*x + c*x^2]], x] /; FreeQ[{a,
b, c, d, e}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[2*c*d - b*e, 0]

Rule 206

Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(1*ArcTanh[(Rt[-b, 2]*x)/Rt[a, 2]])/(Rt[a, 2]*Rt[-b, 2]), x]
/; FreeQ[{a, b}, x] && NegQ[a/b] && (GtQ[a, 0] || LtQ[b, 0])

Rubi steps

\begin{align*} \int \frac{\left (3-x+2 x^2\right )^{3/2} \left (2+x+3 x^2-x^3+5 x^4\right )}{5+2 x} \, dx &=\frac{5}{112} (5+2 x)^2 \left (3-x+2 x^2\right )^{5/2}+\frac{1}{224} \int \frac{\left (3-x+2 x^2\right )^{3/2} \left (573-9926 x-14508 x^2-7464 x^3\right )}{5+2 x} \, dx\\ &=-\frac{311}{448} (5+2 x) \left (3-x+2 x^2\right )^{5/2}+\frac{5}{112} (5+2 x)^2 \left (3-x+2 x^2\right )^{5/2}+\frac{\int \frac{\left (3-x+2 x^2\right )^{3/2} \left (-430152+2062560 x+1682400 x^2\right )}{5+2 x} \, dx}{21504}\\ &=\frac{3505}{896} \left (3-x+2 x^2\right )^{5/2}-\frac{311}{448} (5+2 x) \left (3-x+2 x^2\right )^{5/2}+\frac{5}{112} (5+2 x)^2 \left (3-x+2 x^2\right )^{5/2}+\frac{\int \frac{(24853920-68913600 x) \left (3-x+2 x^2\right )^{3/2}}{5+2 x} \, dx}{860160}\\ &=\frac{(500141-123060 x) \left (3-x+2 x^2\right )^{3/2}}{12288}+\frac{3505}{896} \left (3-x+2 x^2\right )^{5/2}-\frac{311}{448} (5+2 x) \left (3-x+2 x^2\right )^{5/2}+\frac{5}{112} (5+2 x)^2 \left (3-x+2 x^2\right )^{5/2}-\frac{\int \frac{(-29846322240+78902624640 x) \sqrt{3-x+2 x^2}}{5+2 x} \, dx}{55050240}\\ &=\frac{(141051019-23482924 x) \sqrt{3-x+2 x^2}}{65536}+\frac{(500141-123060 x) \left (3-x+2 x^2\right )^{3/2}}{12288}+\frac{3505}{896} \left (3-x+2 x^2\right )^{5/2}-\frac{311}{448} (5+2 x) \left (3-x+2 x^2\right )^{5/2}+\frac{5}{112} (5+2 x)^2 \left (3-x+2 x^2\right )^{5/2}+\frac{\int \frac{21812190368640-43599628289280 x}{(5+2 x) \sqrt{3-x+2 x^2}} \, dx}{1761607680}\\ &=\frac{(141051019-23482924 x) \sqrt{3-x+2 x^2}}{65536}+\frac{(500141-123060 x) \left (3-x+2 x^2\right )^{3/2}}{12288}+\frac{3505}{896} \left (3-x+2 x^2\right )^{5/2}-\frac{311}{448} (5+2 x) \left (3-x+2 x^2\right )^{5/2}+\frac{5}{112} (5+2 x)^2 \left (3-x+2 x^2\right )^{5/2}-\frac{1622009981 \int \frac{1}{\sqrt{3-x+2 x^2}} \, dx}{131072}+\frac{297027}{4} \int \frac{1}{(5+2 x) \sqrt{3-x+2 x^2}} \, dx\\ &=\frac{(141051019-23482924 x) \sqrt{3-x+2 x^2}}{65536}+\frac{(500141-123060 x) \left (3-x+2 x^2\right )^{3/2}}{12288}+\frac{3505}{896} \left (3-x+2 x^2\right )^{5/2}-\frac{311}{448} (5+2 x) \left (3-x+2 x^2\right )^{5/2}+\frac{5}{112} (5+2 x)^2 \left (3-x+2 x^2\right )^{5/2}-\frac{297027}{2} \operatorname{Subst}\left (\int \frac{1}{288-x^2} \, dx,x,\frac{17-22 x}{\sqrt{3-x+2 x^2}}\right )-\frac{1622009981 \operatorname{Subst}\left (\int \frac{1}{\sqrt{1+\frac{x^2}{23}}} \, dx,x,-1+4 x\right )}{131072 \sqrt{46}}\\ &=\frac{(141051019-23482924 x) \sqrt{3-x+2 x^2}}{65536}+\frac{(500141-123060 x) \left (3-x+2 x^2\right )^{3/2}}{12288}+\frac{3505}{896} \left (3-x+2 x^2\right )^{5/2}-\frac{311}{448} (5+2 x) \left (3-x+2 x^2\right )^{5/2}+\frac{5}{112} (5+2 x)^2 \left (3-x+2 x^2\right )^{5/2}+\frac{1622009981 \sinh ^{-1}\left (\frac{1-4 x}{\sqrt{23}}\right )}{131072 \sqrt{2}}-\frac{99009 \tanh ^{-1}\left (\frac{17-22 x}{12 \sqrt{2} \sqrt{3-x+2 x^2}}\right )}{8 \sqrt{2}}\\ \end{align*}

Mathematica [A]  time = 0.187786, size = 101, normalized size = 0.59 \[ \frac{4 \sqrt{2 x^2-x+3} \left (983040 x^6-3710976 x^5+14493696 x^4-46476672 x^3+159973408 x^2-609499532 x+3149403255\right )-34065432576 \sqrt{2} \tanh ^{-1}\left (\frac{17-22 x}{12 \sqrt{4 x^2-2 x+6}}\right )[phone] \sqrt{2} \sinh ^{-1}\left (\frac{1-4 x}{\sqrt{23}}\right )}{5505024} \]

Antiderivative was successfully verified.

[In]

Integrate[((3 - x + 2*x^2)^(3/2)*(2 + x + 3*x^2 - x^3 + 5*x^4))/(5 + 2*x),x]

[Out]

(4*Sqrt[3 - x + 2*x^2]*(3149403255 - 609499532*x + 159973408*x^2 - 46476672*x^3 + 14493696*x^4 - 3710976*x^5 +
983040*x^6) + 34062209601*Sqrt[2]*ArcSinh[(1 - 4*x)/Sqrt[23]] - 34065432576*Sqrt[2]*ArcTanh[(17 - 22*x)/(12*S
qrt[6 - 2*x + 4*x^2])])/5505024

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Maple [A]  time = 0.056, size = 183, normalized size = 1.1 \begin{align*}{\frac{5\,{x}^{2}}{28} \left ( 2\,{x}^{2}-x+3 \right ) ^{{\frac{5}{2}}}}-{\frac{111\,x}{224} \left ( 2\,{x}^{2}-x+3 \right ) ^{{\frac{5}{2}}}}+{\frac{1395}{896} \left ( 2\,{x}^{2}-x+3 \right ) ^{{\frac{5}{2}}}}-{\frac{-10255+41020\,x}{4096} \left ( 2\,{x}^{2}-x+3 \right ) ^{{\frac{3}{2}}}}-{\frac{-707595+2830380\,x}{65536}\sqrt{2\,{x}^{2}-x+3}}-{\frac{1622009981\,\sqrt{2}}{262144}{\it Arcsinh} \left ({\frac{4\,\sqrt{23}}{23} \left ( x-{\frac{1}{4}} \right ) } \right ) }+{\frac{3667}{96} \left ( 2\, \left ( x+5/2 \right ) ^{2}-11\,x-{\frac{19}{2}} \right ) ^{{\frac{3}{2}}}}-{\frac{-40337+161348\,x}{512}\sqrt{2\, \left ( x+5/2 \right ) ^{2}-11\,x-{\frac{19}{2}}}}+{\frac{33003}{16}\sqrt{2\, \left ( x+5/2 \right ) ^{2}-11\,x-{\frac{19}{2}}}}-{\frac{99009\,\sqrt{2}}{16}{\it Artanh} \left ({\frac{\sqrt{2}}{12} \left ({\frac{17}{2}}-11\,x \right ){\frac{1}{\sqrt{2\, \left ( x+5/2 \right ) ^{2}-11\,x-{\frac{19}{2}}}}}} \right ) } \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*x^2-x+3)^(3/2)*(5*x^4-x^3+3*x^2+x+2)/(5+2*x),x)

[Out]

5/28*x^2*(2*x^2-x+3)^(5/2)-111/224*x*(2*x^2-x+3)^(5/2)+1395/896*(2*x^2-x+3)^(5/2)-10255/4096*(-1+4*x)*(2*x^2-x
+3)^(3/2)-707595/65536*(-1+4*x)*(2*x^2-x+3)^(1/2)-1622009981/262144*2^(1/2)*arcsinh(4/23*23^(1/2)*(x-1/4))+366
7/96*(2*(x+5/2)^2-11*x-19/2)^(3/2)-40337/512*(-1+4*x)*(2*(x+5/2)^2-11*x-19/2)^(1/2)+33003/16*(2*(x+5/2)^2-11*x
-19/2)^(1/2)-99009/16*2^(1/2)*arctanh(1/12*(17/2-11*x)*2^(1/2)/(2*(x+5/2)^2-11*x-19/2)^(1/2))

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Maxima [A]  time = 1.61481, size = 212, normalized size = 1.23 \begin{align*} \frac{5}{28} \,{\left (2 \, x^{2} - x + 3\right )}^{\frac{5}{2}} x^{2} - \frac{111}{224} \,{\left (2 \, x^{2} - x + 3\right )}^{\frac{5}{2}} x + \frac{1395}{896} \,{\left (2 \, x^{2} - x + 3\right )}^{\frac{5}{2}} - \frac{10255}{1024} \,{\left (2 \, x^{2} - x + 3\right )}^{\frac{3}{2}} x + \frac{500141}{12288} \,{\left (2 \, x^{2} - x + 3\right )}^{\frac{3}{2}} - \frac{5870731}{16384} \, \sqrt{2 \, x^{2} - x + 3} x - \frac{1622009981}{262144} \, \sqrt{2} \operatorname{arsinh}\left (\frac{4}{23} \, \sqrt{23} x - \frac{1}{23} \, \sqrt{23}\right ) + \frac{99009}{16} \, \sqrt{2} \operatorname{arsinh}\left (\frac{22 \, \sqrt{23} x}{23 \,{\left | 2 \, x + 5 \right |}} - \frac{17 \, \sqrt{23}}{23 \,{\left | 2 \, x + 5 \right |}}\right ) + \frac{141051019}{65536} \, \sqrt{2 \, x^{2} - x + 3} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x^2-x+3)^(3/2)*(5*x^4-x^3+3*x^2+x+2)/(5+2*x),x, algorithm="maxima")

[Out]

5/28*(2*x^2 - x + 3)^(5/2)*x^2 - 111/224*(2*x^2 - x + 3)^(5/2)*x + 1395/896*(2*x^2 - x + 3)^(5/2) - 10255/1024
*(2*x^2 - x + 3)^(3/2)*x + 500141/12288*(2*x^2 - x + 3)^(3/2) - 5870731/16384*sqrt(2*x^2 - x + 3)*x - 16220099
81/262144*sqrt(2)*arcsinh(4/23*sqrt(23)*x - 1/23*sqrt(23)) + 99009/16*sqrt(2)*arcsinh(22/23*sqrt(23)*x/abs(2*x
+ 5) - 17/23*sqrt(23)/abs(2*x + 5)) + 141051019/65536*sqrt(2*x^2 - x + 3)

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Fricas [A]  time = 1.44861, size = 462, normalized size = 2.69 \begin{align*} \frac{1}{1376256} \,{\left (983040 \, x^{6} - 3710976 \, x^{5} + 14493696 \, x^{4} - 46476672 \, x^{3} + 159973408 \, x^{2} - 609499532 \, x + 3149403255\right )} \sqrt{2 \, x^{2} - x + 3} + \frac{1622009981}{524288} \, \sqrt{2} \log \left (4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3}{\left (4 \, x - 1\right )} - 32 \, x^{2} + 16 \, x - 25\right ) + \frac{99009}{32} \, \sqrt{2} \log \left (-\frac{24 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3}{\left (22 \, x - 17\right )} + 1060 \, x^{2} - 1036 \, x + 1153}{4 \, x^{2} + 20 \, x + 25}\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x^2-x+3)^(3/2)*(5*x^4-x^3+3*x^2+x+2)/(5+2*x),x, algorithm="fricas")

[Out]

1/1376256*(983040*x^6 - 3710976*x^5 + 14493696*x^4 - 46476672*x^3 + 159973408*x^2 - 609499532*x + 3149403255)*
sqrt(2*x^2 - x + 3) + 1622009981/524288*sqrt(2)*log(4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x -
25) + 99009/32*sqrt(2)*log(-(24*sqrt(2)*sqrt(2*x^2 - x + 3)*(22*x - 17) + 1060*x^2 - 1036*x + 1153)/(4*x^2 + 2
0*x + 25))

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Sympy [F]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\left (2 x^{2} - x + 3\right )^{\frac{3}{2}} \left (5 x^{4} - x^{3} + 3 x^{2} + x + 2\right )}{2 x + 5}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x**2-x+3)**(3/2)*(5*x**4-x**3+3*x**2+x+2)/(5+2*x),x)

[Out]

Integral((2*x**2 - x + 3)**(3/2)*(5*x**4 - x**3 + 3*x**2 + x + 2)/(2*x + 5), x)

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Giac [A]  time = 1.2201, size = 188, normalized size = 1.09 \begin{align*} \frac{1}{1376256} \,{\left (4 \,{\left (8 \,{\left (12 \,{\left (16 \,{\left (4 \,{\left (40 \, x - 151\right )} x + 2359\right )} x - 121033\right )} x + 4999169\right )} x - 152374883\right )} x + 3149403255\right )} \sqrt{2 \, x^{2} - x + 3} + \frac{1622009981}{262144} \, \sqrt{2} \log \left (-4 \, \sqrt{2} x + \sqrt{2} + 4 \, \sqrt{2 \, x^{2} - x + 3}\right ) - \frac{99009}{16} \, \sqrt{2} \log \left ({\left | -2 \, \sqrt{2} x + \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right |}\right ) + \frac{99009}{16} \, \sqrt{2} \log \left ({\left | -2 \, \sqrt{2} x - 11 \, \sqrt{2} + 2 \, \sqrt{2 \, x^{2} - x + 3} \right |}\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x^2-x+3)^(3/2)*(5*x^4-x^3+3*x^2+x+2)/(5+2*x),x, algorithm="giac")

[Out]

1/1376256*(4*(8*(12*(16*(4*(40*x - 151)*x + 2359)*x - 121033)*x + 4999169)*x - 152374883)*x + 3149403255)*sqrt
(2*x^2 - x + 3) + 1622009981/262144*sqrt(2)*log(-4*sqrt(2)*x + sqrt(2) + 4*sqrt(2*x^2 - x + 3)) - 99009/16*sqr
t(2)*log(abs(-2*sqrt(2)*x + sqrt(2) + 2*sqrt(2*x^2 - x + 3))) + 99009/16*sqrt(2)*log(abs(-2*sqrt(2)*x - 11*sqr
t(2) + 2*sqrt(2*x^2 - x + 3)))