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

Optimal. Leaf size=133 \[ -\frac {(x+8) \left (3 x^2+2\right )^{5/2}}{6 (2 x+3)^3}+\frac {5 (12 x+37) \left (3 x^2+2\right )^{3/2}}{12 (2 x+3)^2}-\frac {15 (37 x+119) \sqrt {3 x^2+2}}{8 (2 x+3)}+\frac {3657}{16} \sqrt {\frac {5}{7}} \tanh ^{-1}\left (\frac {4-9 x}{\sqrt {35} \sqrt {3 x^2+2}}\right )+\frac {1785}{16} \sqrt {3} \sinh ^{-1}\left (\sqrt {\frac {3}{2}} x\right ) \]

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Rubi [A]  time = 0.08, antiderivative size = 133, normalized size of antiderivative = 1.00, number of steps used = 7, number of rules used = 5, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.208, Rules used = {813, 844, 215, 725, 206} \begin {gather*} -\frac {(x+8) \left (3 x^2+2\right )^{5/2}}{6 (2 x+3)^3}+\frac {5 (12 x+37) \left (3 x^2+2\right )^{3/2}}{12 (2 x+3)^2}-\frac {15 (37 x+119) \sqrt {3 x^2+2}}{8 (2 x+3)}+\frac {3657}{16} \sqrt {\frac {5}{7}} \tanh ^{-1}\left (\frac {4-9 x}{\sqrt {35} \sqrt {3 x^2+2}}\right )+\frac {1785}{16} \sqrt {3} \sinh ^{-1}\left (\sqrt {\frac {3}{2}} x\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(-15*(119 + 37*x)*Sqrt[2 + 3*x^2])/(8*(3 + 2*x)) + (5*(37 + 12*x)*(2 + 3*x^2)^(3/2))/(12*(3 + 2*x)^2) - ((8 +
x)*(2 + 3*x^2)^(5/2))/(6*(3 + 2*x)^3) + (1785*Sqrt[3]*ArcSinh[Sqrt[3/2]*x])/16 + (3657*Sqrt[5/7]*ArcTanh[(4 -
9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/16

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 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 725

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

Rule 813

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

Rule 844

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

Rubi steps

\begin {align*} \int \frac {(5-x) \left (2+3 x^2\right )^{5/2}}{(3+2 x)^4} \, dx &=-\frac {(8+x) \left (2+3 x^2\right )^{5/2}}{6 (3+2 x)^3}-\frac {5}{72} \int \frac {(24-288 x) \left (2+3 x^2\right )^{3/2}}{(3+2 x)^3} \, dx\\ &=\frac {5 (37+12 x) \left (2+3 x^2\right )^{3/2}}{12 (3+2 x)^2}-\frac {(8+x) \left (2+3 x^2\right )^{5/2}}{6 (3+2 x)^3}+\frac {5}{768} \int \frac {(4608-21312 x) \sqrt {2+3 x^2}}{(3+2 x)^2} \, dx\\ &=-\frac {15 (119+37 x) \sqrt {2+3 x^2}}{8 (3+2 x)}+\frac {5 (37+12 x) \left (2+3 x^2\right )^{3/2}}{12 (3+2 x)^2}-\frac {(8+x) \left (2+3 x^2\right )^{5/2}}{6 (3+2 x)^3}-\frac {5 \int \frac {170496-822528 x}{(3+2 x) \sqrt {2+3 x^2}} \, dx}{6144}\\ &=-\frac {15 (119+37 x) \sqrt {2+3 x^2}}{8 (3+2 x)}+\frac {5 (37+12 x) \left (2+3 x^2\right )^{3/2}}{12 (3+2 x)^2}-\frac {(8+x) \left (2+3 x^2\right )^{5/2}}{6 (3+2 x)^3}+\frac {5355}{16} \int \frac {1}{\sqrt {2+3 x^2}} \, dx-\frac {18285}{16} \int \frac {1}{(3+2 x) \sqrt {2+3 x^2}} \, dx\\ &=-\frac {15 (119+37 x) \sqrt {2+3 x^2}}{8 (3+2 x)}+\frac {5 (37+12 x) \left (2+3 x^2\right )^{3/2}}{12 (3+2 x)^2}-\frac {(8+x) \left (2+3 x^2\right )^{5/2}}{6 (3+2 x)^3}+\frac {1785}{16} \sqrt {3} \sinh ^{-1}\left (\sqrt {\frac {3}{2}} x\right )+\frac {18285}{16} \operatorname {Subst}\left (\int \frac {1}{35-x^2} \, dx,x,\frac {4-9 x}{\sqrt {2+3 x^2}}\right )\\ &=-\frac {15 (119+37 x) \sqrt {2+3 x^2}}{8 (3+2 x)}+\frac {5 (37+12 x) \left (2+3 x^2\right )^{3/2}}{12 (3+2 x)^2}-\frac {(8+x) \left (2+3 x^2\right )^{5/2}}{6 (3+2 x)^3}+\frac {1785}{16} \sqrt {3} \sinh ^{-1}\left (\sqrt {\frac {3}{2}} x\right )+\frac {3657}{16} \sqrt {\frac {5}{7}} \tanh ^{-1}\left (\frac {4-9 x}{\sqrt {35} \sqrt {2+3 x^2}}\right )\\ \end {align*}

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Mathematica [A]  time = 0.16, size = 97, normalized size = 0.73 \begin {gather*} \frac {1}{336} \left (10971 \sqrt {35} \tanh ^{-1}\left (\frac {4-9 x}{\sqrt {35} \sqrt {3 x^2+2}}\right )-\frac {14 \sqrt {3 x^2+2} \left (36 x^5-432 x^4+3408 x^3+37974 x^2+77061 x+46103\right )}{(2 x+3)^3}+37485 \sqrt {3} \sinh ^{-1}\left (\sqrt {\frac {3}{2}} x\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

((-14*Sqrt[2 + 3*x^2]*(46103 + 77061*x + 37974*x^2 + 3408*x^3 - 432*x^4 + 36*x^5))/(3 + 2*x)^3 + 37485*Sqrt[3]
*ArcSinh[Sqrt[3/2]*x] + 10971*Sqrt[35]*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/336

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IntegrateAlgebraic [A]  time = 1.05, size = 128, normalized size = 0.96 \begin {gather*} -\frac {1785}{16} \sqrt {3} \log \left (\sqrt {3 x^2+2}-\sqrt {3} x\right )-\frac {3657}{8} \sqrt {\frac {5}{7}} \tanh ^{-1}\left (-\frac {2 \sqrt {3 x^2+2}}{\sqrt {35}}+2 \sqrt {\frac {3}{35}} x+3 \sqrt {\frac {3}{35}}\right )+\frac {\sqrt {3 x^2+2} \left (-36 x^5+432 x^4-3408 x^3-37974 x^2-77061 x-46103\right )}{24 (2 x+3)^3} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(Sqrt[2 + 3*x^2]*(-46103 - 77061*x - 37974*x^2 - 3408*x^3 + 432*x^4 - 36*x^5))/(24*(3 + 2*x)^3) - (3657*Sqrt[5
/7]*ArcTanh[3*Sqrt[3/35] + 2*Sqrt[3/35]*x - (2*Sqrt[2 + 3*x^2])/Sqrt[35]])/8 - (1785*Sqrt[3]*Log[-(Sqrt[3]*x)
+ Sqrt[2 + 3*x^2]])/16

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fricas [A]  time = 0.44, size = 167, normalized size = 1.26 \begin {gather*} \frac {10971 \, \sqrt {7} \sqrt {5} {\left (8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right )} \log \left (\frac {\sqrt {7} \sqrt {5} \sqrt {3 \, x^{2} + 2} {\left (9 \, x - 4\right )} - 93 \, x^{2} + 36 \, x - 43}{4 \, x^{2} + 12 \, x + 9}\right ) + 37485 \, \sqrt {3} {\left (8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right )} \log \left (-\sqrt {3} \sqrt {3 \, x^{2} + 2} x - 3 \, x^{2} - 1\right ) - 28 \, {\left (36 \, x^{5} - 432 \, x^{4} + 3408 \, x^{3} + 37974 \, x^{2} + 77061 \, x + 46103\right )} \sqrt {3 \, x^{2} + 2}}{672 \, {\left (8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/672*(10971*sqrt(7)*sqrt(5)*(8*x^3 + 36*x^2 + 54*x + 27)*log((sqrt(7)*sqrt(5)*sqrt(3*x^2 + 2)*(9*x - 4) - 93*
x^2 + 36*x - 43)/(4*x^2 + 12*x + 9)) + 37485*sqrt(3)*(8*x^3 + 36*x^2 + 54*x + 27)*log(-sqrt(3)*sqrt(3*x^2 + 2)
*x - 3*x^2 - 1) - 28*(36*x^5 - 432*x^4 + 3408*x^3 + 37974*x^2 + 77061*x + 46103)*sqrt(3*x^2 + 2))/(8*x^3 + 36*
x^2 + 54*x + 27)

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giac [B]  time = 0.37, size = 275, normalized size = 2.07 \begin {gather*} -\frac {1}{32} \, {\left (3 \, {\left (2 \, x - 33\right )} x + 973\right )} \sqrt {3 \, x^{2} + 2} - \frac {1785}{16} \, \sqrt {3} \log \left (-\sqrt {3} x + \sqrt {3 \, x^{2} + 2}\right ) - \frac {3657}{112} \, \sqrt {35} \log \left (-\frac {{\left | -2 \, \sqrt {3} x - \sqrt {35} - 3 \, \sqrt {3} + 2 \, \sqrt {3 \, x^{2} + 2} \right |}}{2 \, \sqrt {3} x - \sqrt {35} + 3 \, \sqrt {3} - 2 \, \sqrt {3 \, x^{2} + 2}}\right ) - \frac {\sqrt {3} {\left (40667 \, \sqrt {3} {\left (\sqrt {3} x - \sqrt {3 \, x^{2} + 2}\right )}^{5} + 589140 \, {\left (\sqrt {3} x - \sqrt {3 \, x^{2} + 2}\right )}^{4} + 467730 \, \sqrt {3} {\left (\sqrt {3} x - \sqrt {3 \, x^{2} + 2}\right )}^{3} - 1939920 \, {\left (\sqrt {3} x - \sqrt {3 \, x^{2} + 2}\right )}^{2} + 585700 \, \sqrt {3} {\left (\sqrt {3} x - \sqrt {3 \, x^{2} + 2}\right )} - 166304\right )}}{128 \, {\left ({\left (\sqrt {3} x - \sqrt {3 \, x^{2} + 2}\right )}^{2} + 3 \, \sqrt {3} {\left (\sqrt {3} x - \sqrt {3 \, x^{2} + 2}\right )} - 2\right )}^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1/32*(3*(2*x - 33)*x + 973)*sqrt(3*x^2 + 2) - 1785/16*sqrt(3)*log(-sqrt(3)*x + sqrt(3*x^2 + 2)) - 3657/112*sq
rt(35)*log(-abs(-2*sqrt(3)*x - sqrt(35) - 3*sqrt(3) + 2*sqrt(3*x^2 + 2))/(2*sqrt(3)*x - sqrt(35) + 3*sqrt(3) -
2*sqrt(3*x^2 + 2))) - 1/128*sqrt(3)*(40667*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^5 + 589140*(sqrt(3)*x - sqrt
(3*x^2 + 2))^4 + 467730*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2))^3 - 1939920*(sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 58
5700*sqrt(3)*(sqrt(3)*x - sqrt(3*x^2 + 2)) - 166304)/((sqrt(3)*x - sqrt(3*x^2 + 2))^2 + 3*sqrt(3)*(sqrt(3)*x -
sqrt(3*x^2 + 2)) - 2)^3

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maple [A]  time = 0.07, size = 206, normalized size = 1.55 \begin {gather*} \frac {591 \left (-9 x +3 \left (x +\frac {3}{2}\right )^{2}-\frac {19}{4}\right )^{\frac {3}{2}} x}{490}+\frac {1143 \sqrt {-9 x +3 \left (x +\frac {3}{2}\right )^{2}-\frac {19}{4}}\, x}{56}+\frac {8457 \left (-9 x +3 \left (x +\frac {3}{2}\right )^{2}-\frac {19}{4}\right )^{\frac {5}{2}} x}{85750}+\frac {1785 \sqrt {3}\, \arcsinh \left (\frac {\sqrt {6}\, x}{2}\right )}{16}+\frac {3657 \sqrt {35}\, \arctanh \left (\frac {2 \left (-9 x +4\right ) \sqrt {35}}{35 \sqrt {-36 x +12 \left (x +\frac {3}{2}\right )^{2}-19}}\right )}{112}+\frac {37 \left (-9 x +3 \left (x +\frac {3}{2}\right )^{2}-\frac {19}{4}\right )^{\frac {7}{2}}}{4900 \left (x +\frac {3}{2}\right )^{2}}-\frac {2819 \left (-9 x +3 \left (x +\frac {3}{2}\right )^{2}-\frac {19}{4}\right )^{\frac {7}{2}}}{85750 \left (x +\frac {3}{2}\right )}-\frac {7314 \left (-9 x +3 \left (x +\frac {3}{2}\right )^{2}-\frac {19}{4}\right )^{\frac {5}{2}}}{42875}-\frac {1219 \left (-9 x +3 \left (x +\frac {3}{2}\right )^{2}-\frac {19}{4}\right )^{\frac {3}{2}}}{490}-\frac {3657 \sqrt {-36 x +12 \left (x +\frac {3}{2}\right )^{2}-19}}{112}-\frac {13 \left (-9 x +3 \left (x +\frac {3}{2}\right )^{2}-\frac {19}{4}\right )^{\frac {7}{2}}}{840 \left (x +\frac {3}{2}\right )^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

37/4900/(x+3/2)^2*(-9*x+3*(x+3/2)^2-19/4)^(7/2)-2819/85750/(x+3/2)*(-9*x+3*(x+3/2)^2-19/4)^(7/2)-7314/42875*(-
9*x+3*(x+3/2)^2-19/4)^(5/2)+591/490*(-9*x+3*(x+3/2)^2-19/4)^(3/2)*x+1143/56*(-9*x+3*(x+3/2)^2-19/4)^(1/2)*x+17
85/16*arcsinh(1/2*6^(1/2)*x)*3^(1/2)-1219/490*(-9*x+3*(x+3/2)^2-19/4)^(3/2)-3657/112*(-36*x+12*(x+3/2)^2-19)^(
1/2)+3657/112*35^(1/2)*arctanh(2/35*(-9*x+4)*35^(1/2)/(-36*x+12*(x+3/2)^2-19)^(1/2))+8457/85750*(-9*x+3*(x+3/2
)^2-19/4)^(5/2)*x-13/840/(x+3/2)^3*(-9*x+3*(x+3/2)^2-19/4)^(7/2)

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maxima [A]  time = 1.44, size = 173, normalized size = 1.30 \begin {gather*} -\frac {111}{4900} \, {\left (3 \, x^{2} + 2\right )}^{\frac {5}{2}} - \frac {13 \, {\left (3 \, x^{2} + 2\right )}^{\frac {7}{2}}}{105 \, {\left (8 \, x^{3} + 36 \, x^{2} + 54 \, x + 27\right )}} + \frac {37 \, {\left (3 \, x^{2} + 2\right )}^{\frac {7}{2}}}{1225 \, {\left (4 \, x^{2} + 12 \, x + 9\right )}} + \frac {591}{490} \, {\left (3 \, x^{2} + 2\right )}^{\frac {3}{2}} x - \frac {1219}{490} \, {\left (3 \, x^{2} + 2\right )}^{\frac {3}{2}} - \frac {2819 \, {\left (3 \, x^{2} + 2\right )}^{\frac {5}{2}}}{4900 \, {\left (2 \, x + 3\right )}} + \frac {1143}{56} \, \sqrt {3 \, x^{2} + 2} x + \frac {1785}{16} \, \sqrt {3} \operatorname {arsinh}\left (\frac {1}{2} \, \sqrt {6} x\right ) - \frac {3657}{112} \, \sqrt {35} \operatorname {arsinh}\left (\frac {3 \, \sqrt {6} x}{2 \, {\left | 2 \, x + 3 \right |}} - \frac {2 \, \sqrt {6}}{3 \, {\left | 2 \, x + 3 \right |}}\right ) - \frac {3657}{56} \, \sqrt {3 \, x^{2} + 2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-111/4900*(3*x^2 + 2)^(5/2) - 13/105*(3*x^2 + 2)^(7/2)/(8*x^3 + 36*x^2 + 54*x + 27) + 37/1225*(3*x^2 + 2)^(7/2
)/(4*x^2 + 12*x + 9) + 591/490*(3*x^2 + 2)^(3/2)*x - 1219/490*(3*x^2 + 2)^(3/2) - 2819/4900*(3*x^2 + 2)^(5/2)/
(2*x + 3) + 1143/56*sqrt(3*x^2 + 2)*x + 1785/16*sqrt(3)*arcsinh(1/2*sqrt(6)*x) - 3657/112*sqrt(35)*arcsinh(3/2
*sqrt(6)*x/abs(2*x + 3) - 2/3*sqrt(6)/abs(2*x + 3)) - 3657/56*sqrt(3*x^2 + 2)

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mupad [B]  time = 0.12, size = 161, normalized size = 1.21 \begin {gather*} \frac {1785\,\sqrt {3}\,\mathrm {asinh}\left (\frac {\sqrt {2}\,\sqrt {3}\,x}{2}\right )}{16}-\frac {973\,\sqrt {3}\,\sqrt {x^2+\frac {2}{3}}}{32}-\frac {3657\,\sqrt {35}\,\ln \left (x+\frac {3}{2}\right )}{112}+\frac {3657\,\sqrt {35}\,\ln \left (x-\frac {\sqrt {3}\,\sqrt {35}\,\sqrt {x^2+\frac {2}{3}}}{9}-\frac {4}{9}\right )}{112}-\frac {3\,\sqrt {3}\,x^2\,\sqrt {x^2+\frac {2}{3}}}{16}-\frac {5197\,\sqrt {3}\,\sqrt {x^2+\frac {2}{3}}}{64\,\left (x+\frac {3}{2}\right )}+\frac {9485\,\sqrt {3}\,\sqrt {x^2+\frac {2}{3}}}{256\,\left (x^2+3\,x+\frac {9}{4}\right )}+\frac {99\,\sqrt {3}\,x\,\sqrt {x^2+\frac {2}{3}}}{32}-\frac {15925\,\sqrt {3}\,\sqrt {x^2+\frac {2}{3}}}{1536\,\left (x^3+\frac {9\,x^2}{2}+\frac {27\,x}{4}+\frac {27}{8}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

(1785*3^(1/2)*asinh((2^(1/2)*3^(1/2)*x)/2))/16 - (973*3^(1/2)*(x^2 + 2/3)^(1/2))/32 - (3657*35^(1/2)*log(x + 3
/2))/112 + (3657*35^(1/2)*log(x - (3^(1/2)*35^(1/2)*(x^2 + 2/3)^(1/2))/9 - 4/9))/112 - (3*3^(1/2)*x^2*(x^2 + 2
/3)^(1/2))/16 - (5197*3^(1/2)*(x^2 + 2/3)^(1/2))/(64*(x + 3/2)) + (9485*3^(1/2)*(x^2 + 2/3)^(1/2))/(256*(3*x +
x^2 + 9/4)) + (99*3^(1/2)*x*(x^2 + 2/3)^(1/2))/32 - (15925*3^(1/2)*(x^2 + 2/3)^(1/2))/(1536*((27*x)/4 + (9*x^
2)/2 + x^3 + 27/8))

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

[Out]

Timed out

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