3.1417 \(\int \frac {5-x}{(3+2 x)^5 (2+3 x^2)^{3/2}} \, dx\)

Optimal. Leaf size=148 \[ \frac {41 x+26}{70 (2 x+3)^4 \sqrt {3 x^2+2}}-\frac {14944 \sqrt {3 x^2+2}}{1500625 (2 x+3)}-\frac {708 \sqrt {3 x^2+2}}{42875 (2 x+3)^2}-\frac {298 \sqrt {3 x^2+2}}{18375 (2 x+3)^3}+\frac {58 \sqrt {3 x^2+2}}{1225 (2 x+3)^4}-\frac {30078 \tanh ^{-1}\left (\frac {4-9 x}{\sqrt {35} \sqrt {3 x^2+2}}\right )}{1500625 \sqrt {35}} \]

[Out]

-30078/52521875*arctanh(1/35*(4-9*x)*35^(1/2)/(3*x^2+2)^(1/2))*35^(1/2)+1/70*(26+41*x)/(3+2*x)^4/(3*x^2+2)^(1/
2)+58/1225*(3*x^2+2)^(1/2)/(3+2*x)^4-298/18375*(3*x^2+2)^(1/2)/(3+2*x)^3-708/42875*(3*x^2+2)^(1/2)/(3+2*x)^2-1
4944/1500625*(3*x^2+2)^(1/2)/(3+2*x)

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Rubi [A]  time = 0.09, antiderivative size = 148, 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 = {823, 835, 807, 725, 206} \[ \frac {41 x+26}{70 (2 x+3)^4 \sqrt {3 x^2+2}}-\frac {14944 \sqrt {3 x^2+2}}{1500625 (2 x+3)}-\frac {708 \sqrt {3 x^2+2}}{42875 (2 x+3)^2}-\frac {298 \sqrt {3 x^2+2}}{18375 (2 x+3)^3}+\frac {58 \sqrt {3 x^2+2}}{1225 (2 x+3)^4}-\frac {30078 \tanh ^{-1}\left (\frac {4-9 x}{\sqrt {35} \sqrt {3 x^2+2}}\right )}{1500625 \sqrt {35}} \]

Antiderivative was successfully verified.

[In]

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

[Out]

(26 + 41*x)/(70*(3 + 2*x)^4*Sqrt[2 + 3*x^2]) + (58*Sqrt[2 + 3*x^2])/(1225*(3 + 2*x)^4) - (298*Sqrt[2 + 3*x^2])
/(18375*(3 + 2*x)^3) - (708*Sqrt[2 + 3*x^2])/(42875*(3 + 2*x)^2) - (14944*Sqrt[2 + 3*x^2])/(1500625*(3 + 2*x))
- (30078*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(1500625*Sqrt[35])

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 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 807

Int[((d_.) + (e_.)*(x_))^(m_)*((f_.) + (g_.)*(x_))*((a_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :> -Simp[((e*f - d*g
)*(d + e*x)^(m + 1)*(a + c*x^2)^(p + 1))/(2*(p + 1)*(c*d^2 + a*e^2)), x] + Dist[(c*d*f + a*e*g)/(c*d^2 + a*e^2
), Int[(d + e*x)^(m + 1)*(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]
&& EqQ[Simplify[m + 2*p + 3], 0]

Rule 823

Int[((d_.) + (e_.)*(x_))^(m_)*((f_.) + (g_.)*(x_))*((a_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> -Simp[((d + e*x)^(
m + 1)*(f*a*c*e - a*g*c*d + c*(c*d*f + a*e*g)*x)*(a + c*x^2)^(p + 1))/(2*a*c*(p + 1)*(c*d^2 + a*e^2)), x] + Di
st[1/(2*a*c*(p + 1)*(c*d^2 + a*e^2)), Int[(d + e*x)^m*(a + c*x^2)^(p + 1)*Simp[f*(c^2*d^2*(2*p + 3) + a*c*e^2*
(m + 2*p + 3)) - a*c*d*e*g*m + c*e*(c*d*f + a*e*g)*(m + 2*p + 4)*x, x], x], x] /; FreeQ[{a, c, d, e, f, g}, x]
&& NeQ[c*d^2 + a*e^2, 0] && LtQ[p, -1] && (IntegerQ[m] || IntegerQ[p] || IntegersQ[2*m, 2*p])

Rule 835

Int[((d_.) + (e_.)*(x_))^(m_)*((f_.) + (g_.)*(x_))*((a_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :> Simp[((e*f - d*g)
*(d + e*x)^(m + 1)*(a + c*x^2)^(p + 1))/((m + 1)*(c*d^2 + a*e^2)), x] + Dist[1/((m + 1)*(c*d^2 + a*e^2)), Int[
(d + e*x)^(m + 1)*(a + c*x^2)^p*Simp[(c*d*f + a*e*g)*(m + 1) - c*(e*f - d*g)*(m + 2*p + 3)*x, x], x], x] /; Fr
eeQ[{a, c, d, e, f, g, p}, x] && NeQ[c*d^2 + a*e^2, 0] && LtQ[m, -1] && (IntegerQ[m] || IntegerQ[p] || Integer
sQ[2*m, 2*p])

Rubi steps

\begin {align*} \int \frac {5-x}{(3+2 x)^5 \left (2+3 x^2\right )^{3/2}} \, dx &=\frac {26+41 x}{70 (3+2 x)^4 \sqrt {2+3 x^2}}-\frac {1}{210} \int \frac {-780-984 x}{(3+2 x)^5 \sqrt {2+3 x^2}} \, dx\\ &=\frac {26+41 x}{70 (3+2 x)^4 \sqrt {2+3 x^2}}+\frac {58 \sqrt {2+3 x^2}}{1225 (3+2 x)^4}+\frac {\int \frac {43824+12528 x}{(3+2 x)^4 \sqrt {2+3 x^2}} \, dx}{29400}\\ &=\frac {26+41 x}{70 (3+2 x)^4 \sqrt {2+3 x^2}}+\frac {58 \sqrt {2+3 x^2}}{1225 (3+2 x)^4}-\frac {298 \sqrt {2+3 x^2}}{18375 (3+2 x)^3}-\frac {\int \frac {-1333584+300384 x}{(3+2 x)^3 \sqrt {2+3 x^2}} \, dx}{3087000}\\ &=\frac {26+41 x}{70 (3+2 x)^4 \sqrt {2+3 x^2}}+\frac {58 \sqrt {2+3 x^2}}{1225 (3+2 x)^4}-\frac {298 \sqrt {2+3 x^2}}{18375 (3+2 x)^3}-\frac {708 \sqrt {2+3 x^2}}{42875 (3+2 x)^2}+\frac {\int \frac {21601440-10704960 x}{(3+2 x)^2 \sqrt {2+3 x^2}} \, dx}{216090000}\\ &=\frac {26+41 x}{70 (3+2 x)^4 \sqrt {2+3 x^2}}+\frac {58 \sqrt {2+3 x^2}}{1225 (3+2 x)^4}-\frac {298 \sqrt {2+3 x^2}}{18375 (3+2 x)^3}-\frac {708 \sqrt {2+3 x^2}}{42875 (3+2 x)^2}-\frac {14944 \sqrt {2+3 x^2}}{1500625 (3+2 x)}+\frac {30078 \int \frac {1}{(3+2 x) \sqrt {2+3 x^2}} \, dx}{1500625}\\ &=\frac {26+41 x}{70 (3+2 x)^4 \sqrt {2+3 x^2}}+\frac {58 \sqrt {2+3 x^2}}{1225 (3+2 x)^4}-\frac {298 \sqrt {2+3 x^2}}{18375 (3+2 x)^3}-\frac {708 \sqrt {2+3 x^2}}{42875 (3+2 x)^2}-\frac {14944 \sqrt {2+3 x^2}}{1500625 (3+2 x)}-\frac {30078 \operatorname {Subst}\left (\int \frac {1}{35-x^2} \, dx,x,\frac {4-9 x}{\sqrt {2+3 x^2}}\right )}{1500625}\\ &=\frac {26+41 x}{70 (3+2 x)^4 \sqrt {2+3 x^2}}+\frac {58 \sqrt {2+3 x^2}}{1225 (3+2 x)^4}-\frac {298 \sqrt {2+3 x^2}}{18375 (3+2 x)^3}-\frac {708 \sqrt {2+3 x^2}}{42875 (3+2 x)^2}-\frac {14944 \sqrt {2+3 x^2}}{1500625 (3+2 x)}-\frac {30078 \tanh ^{-1}\left (\frac {4-9 x}{\sqrt {35} \sqrt {2+3 x^2}}\right )}{1500625 \sqrt {35}}\\ \end {align*}

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Mathematica [A]  time = 0.09, size = 80, normalized size = 0.54 \[ \frac {-180468 \sqrt {35} \tanh ^{-1}\left (\frac {4-9 x}{\sqrt {35} \sqrt {3 x^2+2}}\right )-\frac {35 \left (2151936 x^5+11467872 x^4+22188792 x^3+18957672 x^2+8562487 x+4197366\right )}{(2 x+3)^4 \sqrt {3 x^2+2}}}{315131250} \]

Antiderivative was successfully verified.

[In]

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

[Out]

((-35*(4197366 + 8562487*x + 18957672*x^2 + 22188792*x^3 + 11467872*x^4 + 2151936*x^5))/((3 + 2*x)^4*Sqrt[2 +
3*x^2]) - 180468*Sqrt[35]*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/315131250

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fricas [A]  time = 0.56, size = 149, normalized size = 1.01 \[ \frac {90234 \, \sqrt {35} {\left (48 \, x^{6} + 288 \, x^{5} + 680 \, x^{4} + 840 \, x^{3} + 675 \, x^{2} + 432 \, x + 162\right )} \log \left (-\frac {\sqrt {35} \sqrt {3 \, x^{2} + 2} {\left (9 \, x - 4\right )} + 93 \, x^{2} - 36 \, x + 43}{4 \, x^{2} + 12 \, x + 9}\right ) - 35 \, {\left (2151936 \, x^{5} + 11467872 \, x^{4} + 22188792 \, x^{3} + 18957672 \, x^{2} + 8562487 \, x + 4197366\right )} \sqrt {3 \, x^{2} + 2}}{315131250 \, {\left (48 \, x^{6} + 288 \, x^{5} + 680 \, x^{4} + 840 \, x^{3} + 675 \, x^{2} + 432 \, x + 162\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/315131250*(90234*sqrt(35)*(48*x^6 + 288*x^5 + 680*x^4 + 840*x^3 + 675*x^2 + 432*x + 162)*log(-(sqrt(35)*sqrt
(3*x^2 + 2)*(9*x - 4) + 93*x^2 - 36*x + 43)/(4*x^2 + 12*x + 9)) - 35*(2151936*x^5 + 11467872*x^4 + 22188792*x^
3 + 18957672*x^2 + 8562487*x + 4197366)*sqrt(3*x^2 + 2))/(48*x^6 + 288*x^5 + 680*x^4 + 840*x^3 + 675*x^2 + 432
*x + 162)

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giac [A]  time = 0.29, size = 234, normalized size = 1.58 \[ \frac {2}{52521875} \, \sqrt {35} {\left (3736 \, \sqrt {35} \sqrt {3} + 15039 \, \log \left (\sqrt {35} \sqrt {3} - 9\right )\right )} \mathrm {sgn}\left (\frac {1}{2 \, x + 3}\right ) - \frac {\frac {\frac {35 \, {\left (\frac {7 \, {\left (\frac {5 \, {\left (\frac {913}{\mathrm {sgn}\left (\frac {1}{2 \, x + 3}\right )} + \frac {1365}{{\left (2 \, x + 3\right )} \mathrm {sgn}\left (\frac {1}{2 \, x + 3}\right )}\right )}}{2 \, x + 3} + \frac {2646}{\mathrm {sgn}\left (\frac {1}{2 \, x + 3}\right )}\right )}}{2 \, x + 3} + \frac {12858}{\mathrm {sgn}\left (\frac {1}{2 \, x + 3}\right )}\right )}}{2 \, x + 3} - \frac {583956}{\mathrm {sgn}\left (\frac {1}{2 \, x + 3}\right )}}{2 \, x + 3} + \frac {134496}{\mathrm {sgn}\left (\frac {1}{2 \, x + 3}\right )}}{9003750 \, \sqrt {-\frac {18}{2 \, x + 3} + \frac {35}{{\left (2 \, x + 3\right )}^{2}} + 3}} - \frac {30078 \, \sqrt {35} \log \left (\sqrt {35} {\left (\sqrt {-\frac {18}{2 \, x + 3} + \frac {35}{{\left (2 \, x + 3\right )}^{2}} + 3} + \frac {\sqrt {35}}{2 \, x + 3}\right )} - 9\right )}{52521875 \, \mathrm {sgn}\left (\frac {1}{2 \, x + 3}\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2/52521875*sqrt(35)*(3736*sqrt(35)*sqrt(3) + 15039*log(sqrt(35)*sqrt(3) - 9))*sgn(1/(2*x + 3)) - 1/9003750*((3
5*(7*(5*(913/sgn(1/(2*x + 3)) + 1365/((2*x + 3)*sgn(1/(2*x + 3))))/(2*x + 3) + 2646/sgn(1/(2*x + 3)))/(2*x + 3
) + 12858/sgn(1/(2*x + 3)))/(2*x + 3) - 583956/sgn(1/(2*x + 3)))/(2*x + 3) + 134496/sgn(1/(2*x + 3)))/sqrt(-18
/(2*x + 3) + 35/(2*x + 3)^2 + 3) - 30078/52521875*sqrt(35)*log(sqrt(35)*(sqrt(-18/(2*x + 3) + 35/(2*x + 3)^2 +
3) + sqrt(35)/(2*x + 3)) - 9)/sgn(1/(2*x + 3))

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maple [A]  time = 0.10, size = 149, normalized size = 1.01 \[ -\frac {22416 x}{1500625 \sqrt {-9 x +3 \left (x +\frac {3}{2}\right )^{2}-\frac {19}{4}}}-\frac {30078 \sqrt {35}\, \arctanh \left (\frac {2 \left (-9 x +4\right ) \sqrt {35}}{35 \sqrt {-36 x +12 \left (x +\frac {3}{2}\right )^{2}-19}}\right )}{52521875}-\frac {913}{117600 \left (x +\frac {3}{2}\right )^{3} \sqrt {-9 x +3 \left (x +\frac {3}{2}\right )^{2}-\frac {19}{4}}}-\frac {9}{1000 \left (x +\frac {3}{2}\right )^{2} \sqrt {-9 x +3 \left (x +\frac {3}{2}\right )^{2}-\frac {19}{4}}}-\frac {2143}{171500 \left (x +\frac {3}{2}\right ) \sqrt {-9 x +3 \left (x +\frac {3}{2}\right )^{2}-\frac {19}{4}}}+\frac {15039}{1500625 \sqrt {-9 x +3 \left (x +\frac {3}{2}\right )^{2}-\frac {19}{4}}}-\frac {13}{2240 \left (x +\frac {3}{2}\right )^{4} \sqrt {-9 x +3 \left (x +\frac {3}{2}\right )^{2}-\frac {19}{4}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-913/117600/(x+3/2)^3/(-9*x+3*(x+3/2)^2-19/4)^(1/2)-9/1000/(x+3/2)^2/(-9*x+3*(x+3/2)^2-19/4)^(1/2)-2143/171500
/(x+3/2)/(-9*x+3*(x+3/2)^2-19/4)^(1/2)+15039/1500625/(-9*x+3*(x+3/2)^2-19/4)^(1/2)-22416/1500625/(-9*x+3*(x+3/
2)^2-19/4)^(1/2)*x-30078/52521875*35^(1/2)*arctanh(2/35*(-9*x+4)*35^(1/2)/(-36*x+12*(x+3/2)^2-19)^(1/2))-13/22
40/(x+3/2)^4/(-9*x+3*(x+3/2)^2-19/4)^(1/2)

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maxima [B]  time = 1.30, size = 254, normalized size = 1.72 \[ \frac {30078}{52521875} \, \sqrt {35} \operatorname {arsinh}\left (\frac {3 \, \sqrt {6} x}{2 \, {\left | 2 \, x + 3 \right |}} - \frac {2 \, \sqrt {6}}{3 \, {\left | 2 \, x + 3 \right |}}\right ) - \frac {22416 \, x}{1500625 \, \sqrt {3 \, x^{2} + 2}} + \frac {15039}{1500625 \, \sqrt {3 \, x^{2} + 2}} - \frac {13}{140 \, {\left (16 \, \sqrt {3 \, x^{2} + 2} x^{4} + 96 \, \sqrt {3 \, x^{2} + 2} x^{3} + 216 \, \sqrt {3 \, x^{2} + 2} x^{2} + 216 \, \sqrt {3 \, x^{2} + 2} x + 81 \, \sqrt {3 \, x^{2} + 2}\right )}} - \frac {913}{14700 \, {\left (8 \, \sqrt {3 \, x^{2} + 2} x^{3} + 36 \, \sqrt {3 \, x^{2} + 2} x^{2} + 54 \, \sqrt {3 \, x^{2} + 2} x + 27 \, \sqrt {3 \, x^{2} + 2}\right )}} - \frac {9}{250 \, {\left (4 \, \sqrt {3 \, x^{2} + 2} x^{2} + 12 \, \sqrt {3 \, x^{2} + 2} x + 9 \, \sqrt {3 \, x^{2} + 2}\right )}} - \frac {2143}{85750 \, {\left (2 \, \sqrt {3 \, x^{2} + 2} x + 3 \, \sqrt {3 \, x^{2} + 2}\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

30078/52521875*sqrt(35)*arcsinh(3/2*sqrt(6)*x/abs(2*x + 3) - 2/3*sqrt(6)/abs(2*x + 3)) - 22416/1500625*x/sqrt(
3*x^2 + 2) + 15039/1500625/sqrt(3*x^2 + 2) - 13/140/(16*sqrt(3*x^2 + 2)*x^4 + 96*sqrt(3*x^2 + 2)*x^3 + 216*sqr
t(3*x^2 + 2)*x^2 + 216*sqrt(3*x^2 + 2)*x + 81*sqrt(3*x^2 + 2)) - 913/14700/(8*sqrt(3*x^2 + 2)*x^3 + 36*sqrt(3*
x^2 + 2)*x^2 + 54*sqrt(3*x^2 + 2)*x + 27*sqrt(3*x^2 + 2)) - 9/250/(4*sqrt(3*x^2 + 2)*x^2 + 12*sqrt(3*x^2 + 2)*
x + 9*sqrt(3*x^2 + 2)) - 2143/85750/(2*sqrt(3*x^2 + 2)*x + 3*sqrt(3*x^2 + 2))

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mupad [B]  time = 0.14, size = 244, normalized size = 1.65 \[ \frac {30078\,\sqrt {35}\,\ln \left (x+\frac {3}{2}\right )}{52521875}-\frac {30078\,\sqrt {35}\,\ln \left (x-\frac {\sqrt {3}\,\sqrt {35}\,\sqrt {x^2+\frac {2}{3}}}{9}-\frac {4}{9}\right )}{52521875}-\frac {13\,\sqrt {3}\,\sqrt {x^2+\frac {2}{3}}}{19600\,\left (x^4+6\,x^3+\frac {27\,x^2}{2}+\frac {27\,x}{2}+\frac {81}{16}\right )}-\frac {168573\,\sqrt {3}\,\sqrt {x^2+\frac {2}{3}}}{210087500\,\left (x-\frac {\sqrt {6}\,1{}\mathrm {i}}{3}\right )}-\frac {168573\,\sqrt {3}\,\sqrt {x^2+\frac {2}{3}}}{210087500\,\left (x+\frac {\sqrt {6}\,1{}\mathrm {i}}{3}\right )}-\frac {354467\,\sqrt {3}\,\sqrt {x^2+\frac {2}{3}}}{105043750\,\left (x+\frac {3}{2}\right )}-\frac {14499\,\sqrt {3}\,\sqrt {x^2+\frac {2}{3}}}{6002500\,\left (x^2+3\,x+\frac {9}{4}\right )}-\frac {323\,\sqrt {3}\,\sqrt {x^2+\frac {2}{3}}}{205800\,\left (x^3+\frac {9\,x^2}{2}+\frac {27\,x}{4}+\frac {27}{8}\right )}-\frac {\sqrt {3}\,\sqrt {6}\,\sqrt {x^2+\frac {2}{3}}\,36471{}\mathrm {i}}{210087500\,\left (x-\frac {\sqrt {6}\,1{}\mathrm {i}}{3}\right )}+\frac {\sqrt {3}\,\sqrt {6}\,\sqrt {x^2+\frac {2}{3}}\,36471{}\mathrm {i}}{210087500\,\left (x+\frac {\sqrt {6}\,1{}\mathrm {i}}{3}\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

(30078*35^(1/2)*log(x + 3/2))/52521875 - (30078*35^(1/2)*log(x - (3^(1/2)*35^(1/2)*(x^2 + 2/3)^(1/2))/9 - 4/9)
)/52521875 - (13*3^(1/2)*(x^2 + 2/3)^(1/2))/(19600*((27*x)/2 + (27*x^2)/2 + 6*x^3 + x^4 + 81/16)) - (168573*3^
(1/2)*(x^2 + 2/3)^(1/2))/(210087500*(x - (6^(1/2)*1i)/3)) - (168573*3^(1/2)*(x^2 + 2/3)^(1/2))/(210087500*(x +
(6^(1/2)*1i)/3)) - (354467*3^(1/2)*(x^2 + 2/3)^(1/2))/(105043750*(x + 3/2)) - (14499*3^(1/2)*(x^2 + 2/3)^(1/2
))/(6002500*(3*x + x^2 + 9/4)) - (323*3^(1/2)*(x^2 + 2/3)^(1/2))/(205800*((27*x)/4 + (9*x^2)/2 + x^3 + 27/8))
- (3^(1/2)*6^(1/2)*(x^2 + 2/3)^(1/2)*36471i)/(210087500*(x - (6^(1/2)*1i)/3)) + (3^(1/2)*6^(1/2)*(x^2 + 2/3)^(
1/2)*36471i)/(210087500*(x + (6^(1/2)*1i)/3))

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

[Out]

Timed out

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