3.63 \(\int \frac{\sqrt{3-x+2 x^2}}{(2+3 x+5 x^2)^2} \, dx\)
Optimal. Leaf size=188 \[ \frac{\sqrt{2 x^2-x+3} (10 x+3)}{31 \left (5 x^2+3 x+2\right )}+\frac{1}{62} \sqrt{\frac{1}{682} \left (70517+49942 \sqrt{2}\right )} \tan ^{-1}\left (\frac{\sqrt{\frac{11}{31 \left (70517+49942 \sqrt{2}\right )}} \left (\left (973+696 \sqrt{2}\right ) x+277 \sqrt{2}+419\right )}{\sqrt{2 x^2-x+3}}\right )-\frac{1}{62} \sqrt{\frac{1}{682} \left (49942 \sqrt{2}-70517\right )} \tanh ^{-1}\left (\frac{\sqrt{\frac{11}{31 \left (49942 \sqrt{2}-70517\right )}} \left (\left (973-696 \sqrt{2}\right ) x-277 \sqrt{2}+419\right )}{\sqrt{2 x^2-x+3}}\right ) \]
[Out]
((3 + 10*x)*Sqrt[3 - x + 2*x^2])/(31*(2 + 3*x + 5*x^2)) + (Sqrt[(70517 + 49942*Sqrt[2])/682]*ArcTan[(Sqrt[11/(
31*(70517 + 49942*Sqrt[2]))]*(419 + 277*Sqrt[2] + (973 + 696*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/62 - (Sqrt[(-7
0517 + 49942*Sqrt[2])/682]*ArcTanh[(Sqrt[11/(31*(-70517 + 49942*Sqrt[2]))]*(419 - 277*Sqrt[2] + (973 - 696*Sqr
t[2])*x))/Sqrt[3 - x + 2*x^2]])/62
________________________________________________________________________________________
Rubi [A] time = 0.393492, antiderivative size = 188, normalized size of antiderivative = 1.,
number of steps used = 6, number of rules used = 5, integrand size = 27, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.185, Rules used =
{971, 1035, 1029, 206, 204} \[ \frac{\sqrt{2 x^2-x+3} (10 x+3)}{31 \left (5 x^2+3 x+2\right )}+\frac{1}{62} \sqrt{\frac{1}{682} \left (70517+49942 \sqrt{2}\right )} \tan ^{-1}\left (\frac{\sqrt{\frac{11}{31 \left (70517+49942 \sqrt{2}\right )}} \left (\left (973+696 \sqrt{2}\right ) x+277 \sqrt{2}+419\right )}{\sqrt{2 x^2-x+3}}\right )-\frac{1}{62} \sqrt{\frac{1}{682} \left (49942 \sqrt{2}-70517\right )} \tanh ^{-1}\left (\frac{\sqrt{\frac{11}{31 \left (49942 \sqrt{2}-70517\right )}} \left (\left (973-696 \sqrt{2}\right ) x-277 \sqrt{2}+419\right )}{\sqrt{2 x^2-x+3}}\right ) \]
Antiderivative was successfully verified.
[In]
Int[Sqrt[3 - x + 2*x^2]/(2 + 3*x + 5*x^2)^2,x]
[Out]
((3 + 10*x)*Sqrt[3 - x + 2*x^2])/(31*(2 + 3*x + 5*x^2)) + (Sqrt[(70517 + 49942*Sqrt[2])/682]*ArcTan[(Sqrt[11/(
31*(70517 + 49942*Sqrt[2]))]*(419 + 277*Sqrt[2] + (973 + 696*Sqrt[2])*x))/Sqrt[3 - x + 2*x^2]])/62 - (Sqrt[(-7
0517 + 49942*Sqrt[2])/682]*ArcTanh[(Sqrt[11/(31*(-70517 + 49942*Sqrt[2]))]*(419 - 277*Sqrt[2] + (973 - 696*Sqr
t[2])*x))/Sqrt[3 - x + 2*x^2]])/62
Rule 971
Int[((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_)*((d_.) + (e_.)*(x_) + (f_.)*(x_)^2)^(q_), x_Symbol] :> Simp[((b +
2*c*x)*(a + b*x + c*x^2)^(p + 1)*(d + e*x + f*x^2)^q)/((b^2 - 4*a*c)*(p + 1)), x] - Dist[1/((b^2 - 4*a*c)*(p
+ 1)), Int[(a + b*x + c*x^2)^(p + 1)*(d + e*x + f*x^2)^(q - 1)*Simp[2*c*d*(2*p + 3) + b*e*q + (2*b*f*q + 2*c*e
*(2*p + q + 3))*x + 2*c*f*(2*p + 2*q + 3)*x^2, x], x], x] /; FreeQ[{a, b, c, d, e, f}, x] && NeQ[b^2 - 4*a*c,
0] && NeQ[e^2 - 4*d*f, 0] && LtQ[p, -1] && GtQ[q, 0] && !IGtQ[q, 0]
Rule 1035
Int[((g_.) + (h_.)*(x_))/(((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)*Sqrt[(d_.) + (e_.)*(x_) + (f_.)*(x_)^2]), x_Symb
ol] :> With[{q = Rt[(c*d - a*f)^2 - (b*d - a*e)*(c*e - b*f), 2]}, Dist[1/(2*q), Int[Simp[h*(b*d - a*e) - g*(c*
d - a*f - q) - (g*(c*e - b*f) - h*(c*d - a*f + q))*x, x]/((a + b*x + c*x^2)*Sqrt[d + e*x + f*x^2]), x], x] - D
ist[1/(2*q), Int[Simp[h*(b*d - a*e) - g*(c*d - a*f + q) - (g*(c*e - b*f) - h*(c*d - a*f - q))*x, x]/((a + b*x
+ c*x^2)*Sqrt[d + e*x + f*x^2]), x], x]] /; FreeQ[{a, b, c, d, e, f, g, h}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[e
^2 - 4*d*f, 0] && NeQ[b*d - a*e, 0] && NegQ[b^2 - 4*a*c]
Rule 1029
Int[((g_.) + (h_.)*(x_))/(((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)*Sqrt[(d_.) + (e_.)*(x_) + (f_.)*(x_)^2]), x_Symb
ol] :> Dist[-2*g*(g*b - 2*a*h), Subst[Int[1/Simp[g*(g*b - 2*a*h)*(b^2 - 4*a*c) - (b*d - a*e)*x^2, x], x], x, S
imp[g*b - 2*a*h - (b*h - 2*g*c)*x, x]/Sqrt[d + e*x + f*x^2]], x] /; FreeQ[{a, b, c, d, e, f, g, h}, x] && NeQ[
b^2 - 4*a*c, 0] && NeQ[e^2 - 4*d*f, 0] && NeQ[b*d - a*e, 0] && EqQ[h^2*(b*d - a*e) - 2*g*h*(c*d - a*f) + g^2*(
c*e - b*f), 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])
Rule 204
Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> -Simp[ArcTan[(Rt[-b, 2]*x)/Rt[-a, 2]]/(Rt[-a, 2]*Rt[-b, 2]), x] /
; FreeQ[{a, b}, x] && PosQ[a/b] && (LtQ[a, 0] || LtQ[b, 0])
Rubi steps
\begin{align*} \int \frac{\sqrt{3-x+2 x^2}}{\left (2+3 x+5 x^2\right )^2} \, dx &=\frac{(3+10 x) \sqrt{3-x+2 x^2}}{31 \left (2+3 x+5 x^2\right )}-\frac{1}{31} \int \frac{-\frac{63}{2}+11 x}{\sqrt{3-x+2 x^2} \left (2+3 x+5 x^2\right )} \, dx\\ &=\frac{(3+10 x) \sqrt{3-x+2 x^2}}{31 \left (2+3 x+5 x^2\right )}-\frac{\int \frac{\frac{11}{2} \left (85-63 \sqrt{2}\right )-\frac{11}{2} \left (41-22 \sqrt{2}\right ) x}{\sqrt{3-x+2 x^2} \left (2+3 x+5 x^2\right )} \, dx}{682 \sqrt{2}}+\frac{\int \frac{\frac{11}{2} \left (85+63 \sqrt{2}\right )-\frac{11}{2} \left (41+22 \sqrt{2}\right ) x}{\sqrt{3-x+2 x^2} \left (2+3 x+5 x^2\right )} \, dx}{682 \sqrt{2}}\\ &=\frac{(3+10 x) \sqrt{3-x+2 x^2}}{31 \left (2+3 x+5 x^2\right )}-\frac{1}{248} \left (11 \left (99884-70517 \sqrt{2}\right )\right ) \operatorname{Subst}\left (\int \frac{1}{-\frac{3751}{4} \left (70517-49942 \sqrt{2}\right )-11 x^2} \, dx,x,\frac{\frac{11}{2} \left (419-277 \sqrt{2}\right )+\frac{11}{2} \left (973-696 \sqrt{2}\right ) x}{\sqrt{3-x+2 x^2}}\right )-\frac{1}{248} \left (11 \left (99884+70517 \sqrt{2}\right )\right ) \operatorname{Subst}\left (\int \frac{1}{-\frac{3751}{4} \left (70517+49942 \sqrt{2}\right )-11 x^2} \, dx,x,\frac{\frac{11}{2} \left (419+277 \sqrt{2}\right )+\frac{11}{2} \left (973+696 \sqrt{2}\right ) x}{\sqrt{3-x+2 x^2}}\right )\\ &=\frac{(3+10 x) \sqrt{3-x+2 x^2}}{31 \left (2+3 x+5 x^2\right )}+\frac{1}{62} \sqrt{\frac{1}{682} \left (70517+49942 \sqrt{2}\right )} \tan ^{-1}\left (\frac{\sqrt{\frac{11}{31 \left (70517+49942 \sqrt{2}\right )}} \left (419+277 \sqrt{2}+\left (973+696 \sqrt{2}\right ) x\right )}{\sqrt{3-x+2 x^2}}\right )-\frac{1}{62} \sqrt{\frac{1}{682} \left (-70517+49942 \sqrt{2}\right )} \tanh ^{-1}\left (\frac{\sqrt{\frac{11}{31 \left (-70517+49942 \sqrt{2}\right )}} \left (419-277 \sqrt{2}+\left (973-696 \sqrt{2}\right ) x\right )}{\sqrt{3-x+2 x^2}}\right )\\ \end{align*}
Mathematica [C] time = 1.08304, size = 214, normalized size = 1.14 \[ \frac{\frac{27280 \sqrt{2 x^2-x+3} (10 x+3)}{5 x^2+3 x+2}+i \sqrt{286-22 i \sqrt{31}} \left (973 \sqrt{31}+1271 i\right ) \tanh ^{-1}\left (\frac{4 i \sqrt{31} x-22 x-i \sqrt{31}+63}{2 \sqrt{286-22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right )-i \sqrt{286+22 i \sqrt{31}} \left (973 \sqrt{31}-1271 i\right ) \tanh ^{-1}\left (\frac{\left (-22-4 i \sqrt{31}\right ) x+i \sqrt{31}+63}{2 \sqrt{286+22 i \sqrt{31}} \sqrt{2 x^2-x+3}}\right )}{845680} \]
Antiderivative was successfully verified.
[In]
Integrate[Sqrt[3 - x + 2*x^2]/(2 + 3*x + 5*x^2)^2,x]
[Out]
((27280*(3 + 10*x)*Sqrt[3 - x + 2*x^2])/(2 + 3*x + 5*x^2) + I*Sqrt[286 - (22*I)*Sqrt[31]]*(1271*I + 973*Sqrt[3
1])*ArcTanh[(63 - I*Sqrt[31] - 22*x + (4*I)*Sqrt[31]*x)/(2*Sqrt[286 - (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])] -
I*Sqrt[286 + (22*I)*Sqrt[31]]*(-1271*I + 973*Sqrt[31])*ArcTanh[(63 + I*Sqrt[31] + (-22 - (4*I)*Sqrt[31])*x)/(
2*Sqrt[286 + (22*I)*Sqrt[31]]*Sqrt[3 - x + 2*x^2])])/845680
________________________________________________________________________________________
Maple [B] time = 0.292, size = 16357, normalized size = 87. \begin{align*} \text{output too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((2*x^2-x+3)^(1/2)/(5*x^2+3*x+2)^2,x)
[Out]
result too large to display
________________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\sqrt{2 \, x^{2} - x + 3}}{{\left (5 \, x^{2} + 3 \, x + 2\right )}^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((2*x^2-x+3)^(1/2)/(5*x^2+3*x+2)^2,x, algorithm="maxima")
[Out]
integrate(sqrt(2*x^2 - x + 3)/(5*x^2 + 3*x + 2)^2, x)
________________________________________________________________________________________
Fricas [B] time = 5.82357, size = 8142, normalized size = 43.31 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((2*x^2-x+3)^(1/2)/(5*x^2+3*x+2)^2,x, algorithm="fricas")
[Out]
-1/186703822445536*(88412*4988406728^(1/4)*sqrt(24971)*sqrt(341)*sqrt(2)*(5*x^2 + 3*x + 2)*sqrt(70517*sqrt(2)
+ 99884)*arctan(1/10668926457462302923*(3096404*sqrt(24971)*(11*4988406728^(3/4)*sqrt(341)*(537184*x^7 - 20478
20*x^6 + 4310846*x^5 - 6853210*x^4 + 3421536*x^3 - 1589328*x^2 - sqrt(2)*(370014*x^7 - 1438653*x^6 + 3014868*x
^5 - 4873381*x^4 + 2452952*x^3 - 1184616*x^2 - 2633472*x + 1893888) - 3787776*x + 2633472) + 774101*4988406728
^(1/4)*sqrt(341)*(40625*x^7 - 622509*x^6 + 3280912*x^5 - 7459052*x^4 + 9621216*x^3 - 5992992*x^2 - sqrt(2)*(28
204*x^7 - 433677*x^6 + 2297444*x^5 - 5257628*x^4 + 6800832*x^3 - 4341024*x^2 - 4810752*x + 3442176) - 6884352*
x + 4810752))*sqrt(2*x^2 - x + 3)*sqrt(70517*sqrt(2) + 99884) + 30285984782473634104*sqrt(31)*sqrt(2)*(28180*x
^8 - 254666*x^7 + 704270*x^6 - 1385256*x^5 + 1549144*x^4 - 642048*x^3 - 98496*x^2 - sqrt(2)*(8746*x^8 - 102335
*x^7 + 396104*x^6 - 783113*x^5 + 1320710*x^4 - 752088*x^3 + 396144*x^2 + 546048*x - 539136) + 1154304*x - 4561
92) - 2*sqrt(49942)*(sqrt(24971)*(11*4988406728^(3/4)*sqrt(341)*(84604*x^7 - 121310*x^6 + 389610*x^5 - 147168*
x^4 + 168912*x^3 + 186624*x^2 - sqrt(2)*(57082*x^7 - 82029*x^6 + 264639*x^5 - 107216*x^4 + 130104*x^3 + 110592
*x^2 - 110592*x) - 186624*x) + 774101*4988406728^(1/4)*sqrt(341)*(6379*x^7 - 82508*x^6 + 318020*x^5 - 410688*x
^4 + 523872*x^3 + 331776*x^2 - sqrt(2)*(4365*x^7 - 56468*x^6 + 217820*x^5 - 282816*x^4 + 366624*x^3 + 207360*x
^2 - 207360*x) - 331776*x))*sqrt(2*x^2 - x + 3)*sqrt(70517*sqrt(2) + 99884) + 425261673562*sqrt(31)*sqrt(2)*(1
23408*x^8 - 914152*x^7 + 1578888*x^6 - 3293072*x^5 + 396480*x^4 + 798336*x^3 - 3822336*x^2 - sqrt(2)*(15550*x^
8 - 118051*x^7 + 244047*x^6 - 707374*x^5 + 1053960*x^4 - 1667952*x^3 + 1209600*x^2 - 1036800*x) + 3276288*x) +
19330076071*sqrt(31)*(254591*x^8 - 4815126*x^7 + 32303580*x^6 - 90866808*x^5 + 108781920*x^4 - 74219328*x^3 -
168956928*x^2 - 15488*sqrt(2)*(4*x^8 - 76*x^7 + 517*x^6 - 1536*x^5 + 2385*x^4 - 3618*x^3 + 2268*x^2 - 1944*x)
+ 144820224*x))*sqrt(-(4988406728^(1/4)*sqrt(24971)*sqrt(341)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(10*x + 3
) - 13*x - 7)*sqrt(70517*sqrt(2) + 99884) - 1175859419*x^2 - 1055873764*sqrt(2)*(2*x^2 - x + 3) + 3623566781*x
- 4799426200)/x^2) + 344158917982654933*sqrt(31)*(2828123*x^8 - 9696916*x^7 + 53385560*x^6 - 142835344*x^5 +
254146592*x^4 - 249300096*x^3 + 37981440*x^2 - 7744*sqrt(2)*(1348*x^8 - 2692*x^7 + 9789*x^6 - 10070*x^5 + 1556
9*x^4 - 5568*x^3 + 1080*x^2 + 4320*x - 5184) + 223064064*x - 94887936))/(2585191*x^8 - 4661200*x^7 + 14191920*
x^6 + 490880*x^5 - 13562944*x^4 + 44249088*x^3 - 34615296*x^2 - 24772608*x + 18579456)) + 88412*4988406728^(1/
4)*sqrt(24971)*sqrt(341)*sqrt(2)*(5*x^2 + 3*x + 2)*sqrt(70517*sqrt(2) + 99884)*arctan(1/10668926457462302923*(
3096404*sqrt(24971)*(11*4988406728^(3/4)*sqrt(341)*(537184*x^7 - 2047820*x^6 + 4310846*x^5 - 6853210*x^4 + 342
1536*x^3 - 1589328*x^2 - sqrt(2)*(370014*x^7 - 1438653*x^6 + 3014868*x^5 - 4873381*x^4 + 2452952*x^3 - 1184616
*x^2 - 2633472*x + 1893888) - 3787776*x + 2633472) + 774101*4988406728^(1/4)*sqrt(341)*(40625*x^7 - 622509*x^6
+ 3280912*x^5 - 7459052*x^4 + 9621216*x^3 - 5992992*x^2 - sqrt(2)*(28204*x^7 - 433677*x^6 + 2297444*x^5 - 525
7628*x^4 + 6800832*x^3 - 4341024*x^2 - 4810752*x + 3442176) - 6884352*x + 4810752))*sqrt(2*x^2 - x + 3)*sqrt(7
0517*sqrt(2) + 99884) - 30285984782473634104*sqrt(31)*sqrt(2)*(28180*x^8 - 254666*x^7 + 704270*x^6 - 1385256*x
^5 + 1549144*x^4 - 642048*x^3 - 98496*x^2 - sqrt(2)*(8746*x^8 - 102335*x^7 + 396104*x^6 - 783113*x^5 + 1320710
*x^4 - 752088*x^3 + 396144*x^2 + 546048*x - 539136) + 1154304*x - 456192) - 2*sqrt(49942)*(sqrt(24971)*(11*498
8406728^(3/4)*sqrt(341)*(84604*x^7 - 121310*x^6 + 389610*x^5 - 147168*x^4 + 168912*x^3 + 186624*x^2 - sqrt(2)*
(57082*x^7 - 82029*x^6 + 264639*x^5 - 107216*x^4 + 130104*x^3 + 110592*x^2 - 110592*x) - 186624*x) + 774101*49
88406728^(1/4)*sqrt(341)*(6379*x^7 - 82508*x^6 + 318020*x^5 - 410688*x^4 + 523872*x^3 + 331776*x^2 - sqrt(2)*(
4365*x^7 - 56468*x^6 + 217820*x^5 - 282816*x^4 + 366624*x^3 + 207360*x^2 - 207360*x) - 331776*x))*sqrt(2*x^2 -
x + 3)*sqrt(70517*sqrt(2) + 99884) - 425261673562*sqrt(31)*sqrt(2)*(123408*x^8 - 914152*x^7 + 1578888*x^6 - 3
293072*x^5 + 396480*x^4 + 798336*x^3 - 3822336*x^2 - sqrt(2)*(15550*x^8 - 118051*x^7 + 244047*x^6 - 707374*x^5
+ 1053960*x^4 - 1667952*x^3 + 1209600*x^2 - 1036800*x) + 3276288*x) - 19330076071*sqrt(31)*(254591*x^8 - 4815
126*x^7 + 32303580*x^6 - 90866808*x^5 + 108781920*x^4 - 74219328*x^3 - 168956928*x^2 - 15488*sqrt(2)*(4*x^8 -
76*x^7 + 517*x^6 - 1536*x^5 + 2385*x^4 - 3618*x^3 + 2268*x^2 - 1944*x) + 144820224*x))*sqrt((4988406728^(1/4)*
sqrt(24971)*sqrt(341)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(10*x + 3) - 13*x - 7)*sqrt(70517*sqrt(2) + 99884)
+ 1175859419*x^2 + 1055873764*sqrt(2)*(2*x^2 - x + 3) - 3623566781*x + 4799426200)/x^2) - 344158917982654933*
sqrt(31)*(2828123*x^8 - 9696916*x^7 + 53385560*x^6 - 142835344*x^5 + 254146592*x^4 - 249300096*x^3 + 37981440*
x^2 - 7744*sqrt(2)*(1348*x^8 - 2692*x^7 + 9789*x^6 - 10070*x^5 + 15569*x^4 - 5568*x^3 + 1080*x^2 + 4320*x - 51
84) + 223064064*x - 94887936))/(2585191*x^8 - 4661200*x^7 + 14191920*x^6 + 490880*x^5 - 13562944*x^4 + 4424908
8*x^3 - 34615296*x^2 - 24772608*x + 18579456)) - 4988406728^(1/4)*sqrt(24971)*sqrt(341)*sqrt(31)*(499420*x^2 -
70517*sqrt(2)*(5*x^2 + 3*x + 2) + 299652*x + 199768)*sqrt(70517*sqrt(2) + 99884)*log(199768*(4988406728^(1/4)
*sqrt(24971)*sqrt(341)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(10*x + 3) - 13*x - 7)*sqrt(70517*sqrt(2) + 99884
) + 1175859419*x^2 + 1055873764*sqrt(2)*(2*x^2 - x + 3) - 3623566781*x + 4799426200)/x^2) + 4988406728^(1/4)*s
qrt(24971)*sqrt(341)*sqrt(31)*(499420*x^2 - 70517*sqrt(2)*(5*x^2 + 3*x + 2) + 299652*x + 199768)*sqrt(70517*sq
rt(2) + 99884)*log(-199768*(4988406728^(1/4)*sqrt(24971)*sqrt(341)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(10*x
+ 3) - 13*x - 7)*sqrt(70517*sqrt(2) + 99884) - 1175859419*x^2 - 1055873764*sqrt(2)*(2*x^2 - x + 3) + 36235667
81*x - 4799426200)/x^2) - 6022703949856*sqrt(2*x^2 - x + 3)*(10*x + 3))/(5*x^2 + 3*x + 2)
________________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\sqrt{2 x^{2} - x + 3}}{\left (5 x^{2} + 3 x + 2\right )^{2}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((2*x**2-x+3)**(1/2)/(5*x**2+3*x+2)**2,x)
[Out]
Integral(sqrt(2*x**2 - x + 3)/(5*x**2 + 3*x + 2)**2, x)
________________________________________________________________________________________
Giac [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: TypeError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((2*x^2-x+3)^(1/2)/(5*x^2+3*x+2)^2,x, algorithm="giac")
[Out]
Exception raised: TypeError