3.2337 \(\int (1-2 x)^{3/2} (2+3 x)^3 (3+5 x)^{3/2} \, dx\)

Optimal. Leaf size=172 \[ -\frac {3}{70} (3 x+2)^2 (5 x+3)^{5/2} (1-2 x)^{5/2}-\frac {141599 (5 x+3)^{3/2} (1-2 x)^{5/2}}{128000}-\frac {3 (5 x+3)^{5/2} (33300 x+49829) (1-2 x)^{5/2}}{280000}-\frac {1557589 \sqrt {5 x+3} (1-2 x)^{5/2}}{512000}+\frac {17133479 \sqrt {5 x+3} (1-2 x)^{3/2}}{10240000}+\frac {565404807 \sqrt {5 x+3} \sqrt {1-2 x}}{102400000}+\frac {6219452877 \sin ^{-1}\left (\sqrt {\frac {2}{11}} \sqrt {5 x+3}\right )}{102400000 \sqrt {10}} \]

[Out]

-141599/128000*(1-2*x)^(5/2)*(3+5*x)^(3/2)-3/70*(1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^(5/2)-3/280000*(1-2*x)^(5/2)*(
3+5*x)^(5/2)*(49829+33300*x)[phone]/1024000000*arcsin(1/11*22^(1/2)*(3+5*x)^(1/2))*10^(1/2)[phone]/10240
000*(1-2*x)^(3/2)*(3+5*x)^(1/2)-1557589/512000*(1-2*x)^(5/2)*(3+5*x)^(1/2)[phone]/102400000*(1-2*x)^(1/2)*(
3+5*x)^(1/2)

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Rubi [A]  time = 0.05, antiderivative size = 172, normalized size of antiderivative = 1.00, number of steps used = 8, number of rules used = 5, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.192, Rules used = {100, 147, 50, 54, 216} \[ -\frac {3}{70} (3 x+2)^2 (5 x+3)^{5/2} (1-2 x)^{5/2}-\frac {141599 (5 x+3)^{3/2} (1-2 x)^{5/2}}{128000}-\frac {3 (5 x+3)^{5/2} (33300 x+49829) (1-2 x)^{5/2}}{280000}-\frac {1557589 \sqrt {5 x+3} (1-2 x)^{5/2}}{512000}+\frac {17133479 \sqrt {5 x+3} (1-2 x)^{3/2}}{10240000}+\frac {565404807 \sqrt {5 x+3} \sqrt {1-2 x}}{102400000}+\frac {6219452877 \sin ^{-1}\left (\sqrt {\frac {2}{11}} \sqrt {5 x+3}\right )}{102400000 \sqrt {10}} \]

Antiderivative was successfully verified.

[In]

Int[(1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x)^(3/2),x]

[Out]

(565404807*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/102400000 + (17133479*(1 - 2*x)^(3/2)*Sqrt[3 + 5*x])/10240000 - (15575
89*(1 - 2*x)^(5/2)*Sqrt[3 + 5*x])/512000 - (141599*(1 - 2*x)^(5/2)*(3 + 5*x)^(3/2))/128000 - (3*(1 - 2*x)^(5/2
)*(2 + 3*x)^2*(3 + 5*x)^(5/2))/70 - (3*(1 - 2*x)^(5/2)*(3 + 5*x)^(5/2)*(49829 + 33300*x))/280000 + (6219452877
*ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]])/(102400000*Sqrt[10])

Rule 50

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

Rule 54

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

Rule 100

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

Rule 147

Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.)*((e_) + (f_.)*(x_))*((g_.) + (h_.)*(x_)), x_Symbol]
:> -Simp[((a*d*f*h*(n + 2) + b*c*f*h*(m + 2) - b*d*(f*g + e*h)*(m + n + 3) - b*d*f*h*(m + n + 2)*x)*(a + b*x)^
(m + 1)*(c + d*x)^(n + 1))/(b^2*d^2*(m + n + 2)*(m + n + 3)), x] + Dist[(a^2*d^2*f*h*(n + 1)*(n + 2) + a*b*d*(
n + 1)*(2*c*f*h*(m + 1) - d*(f*g + e*h)*(m + n + 3)) + b^2*(c^2*f*h*(m + 1)*(m + 2) - c*d*(f*g + e*h)*(m + 1)*
(m + n + 3) + d^2*e*g*(m + n + 2)*(m + n + 3)))/(b^2*d^2*(m + n + 2)*(m + n + 3)), Int[(a + b*x)^m*(c + d*x)^n
, x], x] /; FreeQ[{a, b, c, d, e, f, g, h, m, n}, x] && NeQ[m + n + 2, 0] && NeQ[m + n + 3, 0]

Rule 216

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

Rubi steps

\begin {align*} \int (1-2 x)^{3/2} (2+3 x)^3 (3+5 x)^{3/2} \, dx &=-\frac {3}{70} (1-2 x)^{5/2} (2+3 x)^2 (3+5 x)^{5/2}-\frac {1}{70} \int \left (-319-\frac {999 x}{2}\right ) (1-2 x)^{3/2} (2+3 x) (3+5 x)^{3/2} \, dx\\ &=-\frac {3}{70} (1-2 x)^{5/2} (2+3 x)^2 (3+5 x)^{5/2}-\frac {3 (1-2 x)^{5/2} (3+5 x)^{5/2} (49829+33300 x)}{280000}+\frac {141599 \int (1-2 x)^{3/2} (3+5 x)^{3/2} \, dx}{16000}\\ &=-\frac {141599 (1-2 x)^{5/2} (3+5 x)^{3/2}}{128000}-\frac {3}{70} (1-2 x)^{5/2} (2+3 x)^2 (3+5 x)^{5/2}-\frac {3 (1-2 x)^{5/2} (3+5 x)^{5/2} (49829+33300 x)}{280000}+\frac {4672767 \int (1-2 x)^{3/2} \sqrt {3+5 x} \, dx}{256000}\\ &=-\frac {1557589 (1-2 x)^{5/2} \sqrt {3+5 x}}{512000}-\frac {141599 (1-2 x)^{5/2} (3+5 x)^{3/2}}{128000}-\frac {3}{70} (1-2 x)^{5/2} (2+3 x)^2 (3+5 x)^{5/2}-\frac {3 (1-2 x)^{5/2} (3+5 x)^{5/2} (49829+33300 x)}{280000}+\frac {17133479 \int \frac {(1-2 x)^{3/2}}{\sqrt {3+5 x}} \, dx}{1024000}\\ &=\frac {17133479 (1-2 x)^{3/2} \sqrt {3+5 x}}{10240000}-\frac {1557589 (1-2 x)^{5/2} \sqrt {3+5 x}}{512000}-\frac {141599 (1-2 x)^{5/2} (3+5 x)^{3/2}}{128000}-\frac {3}{70} (1-2 x)^{5/2} (2+3 x)^2 (3+5 x)^{5/2}-\frac {3 (1-2 x)^{5/2} (3+5 x)^{5/2} (49829+33300 x)}{280000}+\frac {565404807 \int \frac {\sqrt {1-2 x}}{\sqrt {3+5 x}} \, dx}{20480000}\\ &=\frac {565404807 \sqrt {1-2 x} \sqrt {3+5 x}}{102400000}+\frac {17133479 (1-2 x)^{3/2} \sqrt {3+5 x}}{10240000}-\frac {1557589 (1-2 x)^{5/2} \sqrt {3+5 x}}{512000}-\frac {141599 (1-2 x)^{5/2} (3+5 x)^{3/2}}{128000}-\frac {3}{70} (1-2 x)^{5/2} (2+3 x)^2 (3+5 x)^{5/2}-\frac {3 (1-2 x)^{5/2} (3+5 x)^{5/2} (49829+33300 x)}{280000}+\frac {6219452877 \int \frac {1}{\sqrt {1-2 x} \sqrt {3+5 x}} \, dx}{204800000}\\ &=\frac {565404807 \sqrt {1-2 x} \sqrt {3+5 x}}{102400000}+\frac {17133479 (1-2 x)^{3/2} \sqrt {3+5 x}}{10240000}-\frac {1557589 (1-2 x)^{5/2} \sqrt {3+5 x}}{512000}-\frac {141599 (1-2 x)^{5/2} (3+5 x)^{3/2}}{128000}-\frac {3}{70} (1-2 x)^{5/2} (2+3 x)^2 (3+5 x)^{5/2}-\frac {3 (1-2 x)^{5/2} (3+5 x)^{5/2} (49829+33300 x)}{280000}+\frac {6219452877 \operatorname {Subst}\left (\int \frac {1}{\sqrt {11-2 x^2}} \, dx,x,\sqrt {3+5 x}\right )}{102400000 \sqrt {5}}\\ &=\frac {565404807 \sqrt {1-2 x} \sqrt {3+5 x}}{102400000}+\frac {17133479 (1-2 x)^{3/2} \sqrt {3+5 x}}{10240000}-\frac {1557589 (1-2 x)^{5/2} \sqrt {3+5 x}}{512000}-\frac {141599 (1-2 x)^{5/2} (3+5 x)^{3/2}}{128000}-\frac {3}{70} (1-2 x)^{5/2} (2+3 x)^2 (3+5 x)^{5/2}-\frac {3 (1-2 x)^{5/2} (3+5 x)^{5/2} (49829+33300 x)}{280000}+\frac {6219452877 \sin ^{-1}\left (\sqrt {\frac {2}{11}} \sqrt {3+5 x}\right )}{102400000 \sqrt {10}}\\ \end {align*}

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Mathematica [A]  time = 0.18, size = 89, normalized size = 0.52 \[ \frac {10 \sqrt {5 x+3} \left (55296000000 x^7+108288000000 x^6+25496064000 x^5-71786259200 x^4-44888000960 x^3+10130684360 x^2+17193258662 x-3952411101\right )[phone] \sqrt {20 x-10} \sinh ^{-1}\left (\sqrt {\frac {5}{11}} \sqrt {2 x-1}\right )}{7168000000 \sqrt {1-2 x}} \]

Antiderivative was successfully verified.

[In]

Integrate[(1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x)^(3/2),x]

[Out]

(10*Sqrt[3 + 5*x]*(-3952411101 + 17193258662*x + 10130684360*x^2 - 44888000960*x^3 - 71786259200*x^4 + 2549606
4000*x^5 + 108288000000*x^6 + 55296000000*x^7) + 43536170139*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x
]])/(7168000000*Sqrt[1 - 2*x])

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fricas [A]  time = 1.07, size = 87, normalized size = 0.51 \[ -\frac {1}{716800000} \, {\left (27648000000 \, x^{6} + 67968000000 \, x^{5} + 46732032000 \, x^{4} - 12527113600 \, x^{3} - 28707557280 \, x^{2} - 9288436460 \, x + 3952411101\right )} \sqrt {5 \, x + 3} \sqrt {-2 \, x + 1} - \frac {6219452877}{2048000000} \, \sqrt {10} \arctan \left (\frac {\sqrt {10} {\left (20 \, x + 1\right )} \sqrt {5 \, x + 3} \sqrt {-2 \, x + 1}}{20 \, {\left (10 \, x^{2} + x - 3\right )}}\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(3/2),x, algorithm="fricas")

[Out]

-1/716800000*(27648000000*x^6 + 67968000000*x^5 + 46732032000*x^4 - 12527113600*x^3 - 28707557280*x^2 - 928843
6460*x + 3952411101)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 6219452877/2048000000*sqrt(10)*arctan(1/20*sqrt(10)*(20*x
+ 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))

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giac [B]  time = 1.29, size = 446, normalized size = 2.59 \[ -\frac {9}{35840000000} \, \sqrt {5} {\left (2 \, {\left (4 \, {\left (8 \, {\left (4 \, {\left (16 \, {\left (20 \, {\left (120 \, x - 443\right )} {\left (5 \, x + 3\right )} + 94933\right )} {\left (5 \, x + 3\right )} - 7838433\right )} {\left (5 \, x + 3\right )} + 98794353\right )} {\left (5 \, x + 3\right )} - 1568443065\right )} {\left (5 \, x + 3\right )} + 8438816295\right )} \sqrt {5 \, x + 3} \sqrt {-10 \, x + 5} + 17534989395 \, \sqrt {2} \arcsin \left (\frac {1}{11} \, \sqrt {22} \sqrt {5 \, x + 3}\right )\right )} - \frac {243}{2560000000} \, \sqrt {5} {\left (2 \, {\left (4 \, {\left (8 \, {\left (4 \, {\left (16 \, {\left (100 \, x - 311\right )} {\left (5 \, x + 3\right )} + 46071\right )} {\left (5 \, x + 3\right )} - 775911\right )} {\left (5 \, x + 3\right )} + 15385695\right )} {\left (5 \, x + 3\right )} - 99422145\right )} \sqrt {5 \, x + 3} \sqrt {-10 \, x + 5} - 220189365 \, \sqrt {2} \arcsin \left (\frac {1}{11} \, \sqrt {22} \sqrt {5 \, x + 3}\right )\right )} - \frac {561}{160000000} \, \sqrt {5} {\left (2 \, {\left (4 \, {\left (8 \, {\left (12 \, {\left (80 \, x - 203\right )} {\left (5 \, x + 3\right )} + 19073\right )} {\left (5 \, x + 3\right )} - 506185\right )} {\left (5 \, x + 3\right )} + 4031895\right )} \sqrt {5 \, x + 3} \sqrt {-10 \, x + 5} + 10392195 \, \sqrt {2} \arcsin \left (\frac {1}{11} \, \sqrt {22} \sqrt {5 \, x + 3}\right )\right )} - \frac {769}{9600000} \, \sqrt {5} {\left (2 \, {\left (4 \, {\left (8 \, {\left (60 \, x - 119\right )} {\left (5 \, x + 3\right )} + 6163\right )} {\left (5 \, x + 3\right )} - 66189\right )} \sqrt {5 \, x + 3} \sqrt {-10 \, x + 5} - 184305 \, \sqrt {2} \arcsin \left (\frac {1}{11} \, \sqrt {22} \sqrt {5 \, x + 3}\right )\right )} + \frac {319}{60000} \, \sqrt {5} {\left (2 \, {\left (4 \, {\left (40 \, x - 59\right )} {\left (5 \, x + 3\right )} + 1293\right )} \sqrt {5 \, x + 3} \sqrt {-10 \, x + 5} + 4785 \, \sqrt {2} \arcsin \left (\frac {1}{11} \, \sqrt {22} \sqrt {5 \, x + 3}\right )\right )} + \frac {21}{100} \, \sqrt {5} {\left (2 \, {\left (20 \, x - 23\right )} \sqrt {5 \, x + 3} \sqrt {-10 \, x + 5} - 143 \, \sqrt {2} \arcsin \left (\frac {1}{11} \, \sqrt {22} \sqrt {5 \, x + 3}\right )\right )} + \frac {36}{25} \, \sqrt {5} {\left (11 \, \sqrt {2} \arcsin \left (\frac {1}{11} \, \sqrt {22} \sqrt {5 \, x + 3}\right ) + 2 \, \sqrt {5 \, x + 3} \sqrt {-10 \, x + 5}\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(3/2),x, algorithm="giac")

[Out]

-9/35840000000*sqrt(5)*(2*(4*(8*(4*(16*(20*(120*x - 443)*(5*x + 3) + 94933)*(5*x + 3) - 7838433)*(5*x + 3) + 9
8794353)*(5*x + 3) - 1568443065)*(5*x + 3) + 8438816295)*sqrt(5*x + 3)*sqrt(-10*x + 5) + 17534989395*sqrt(2)*a
rcsin(1/11*sqrt(22)*sqrt(5*x + 3))) - 243/2560000000*sqrt(5)*(2*(4*(8*(4*(16*(100*x - 311)*(5*x + 3) + 46071)*
(5*x + 3) - 775911)*(5*x + 3) + 15385695)*(5*x + 3) - 99422145)*sqrt(5*x + 3)*sqrt(-10*x + 5) - 220189365*sqrt
(2)*arcsin(1/11*sqrt(22)*sqrt(5*x + 3))) - 561/160000000*sqrt(5)*(2*(4*(8*(12*(80*x - 203)*(5*x + 3) + 19073)*
(5*x + 3) - 506185)*(5*x + 3) + 4031895)*sqrt(5*x + 3)*sqrt(-10*x + 5) + 10392195*sqrt(2)*arcsin(1/11*sqrt(22)
*sqrt(5*x + 3))) - 769/9600000*sqrt(5)*(2*(4*(8*(60*x - 119)*(5*x + 3) + 6163)*(5*x + 3) - 66189)*sqrt(5*x + 3
)*sqrt(-10*x + 5) - 184305*sqrt(2)*arcsin(1/11*sqrt(22)*sqrt(5*x + 3))) + 319/60000*sqrt(5)*(2*(4*(40*x - 59)*
(5*x + 3) + 1293)*sqrt(5*x + 3)*sqrt(-10*x + 5) + 4785*sqrt(2)*arcsin(1/11*sqrt(22)*sqrt(5*x + 3))) + 21/100*s
qrt(5)*(2*(20*x - 23)*sqrt(5*x + 3)*sqrt(-10*x + 5) - 143*sqrt(2)*arcsin(1/11*sqrt(22)*sqrt(5*x + 3))) + 36/25
*sqrt(5)*(11*sqrt(2)*arcsin(1/11*sqrt(22)*sqrt(5*x + 3)) + 2*sqrt(5*x + 3)*sqrt(-10*x + 5))

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maple [A]  time = 0.01, size = 155, normalized size = 0.90 \[ \frac {\sqrt {-2 x +1}\, \sqrt {5 x +3}\, \left (-552960000000 \sqrt {-10 x^{2}-x +3}\, x^{6}-1359360000000 \sqrt {-10 x^{2}-x +3}\, x^{5}-934640640000 \sqrt {-10 x^{2}-x +3}\, x^{4}[phone] \sqrt {-10 x^{2}-x +3}\, x^{3}[phone] \sqrt {-10 x^{2}-x +3}\, x^{2}[phone] \sqrt {-10 x^{2}-x +3}\, x [phone] \sqrt {10}\, \arcsin \left (\frac {20 x}{11}+\frac {1}{11}\right )-79048222020 \sqrt {-10 x^{2}-x +3}\right )}{14336000000 \sqrt {-10 x^{2}-x +3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-2*x+1)^(3/2)*(3*x+2)^3*(5*x+3)^(3/2),x)

[Out]

1/14336000000*(-2*x+1)^(1/2)*(5*x+3)^(1/2)*(-552960000000*(-10*x^2-x+3)^(1/2)*x^6-1359360000000*(-10*x^2-x+3)^
(1/2)*x^5-934640640000*(-10*x^2-x+3)^(1/2)*x^4+250542272000*(-10*x^2-x+3)^(1/2)*x^3+574151145600*(-10*x^2-x+3)
^(1/2)*x^2+43536170139*10^(1/2)*arcsin(20/11*x+1/11)[phone]*(-10*x^2-x+3)^(1/2)*x-79048222020*(-10*x^2-x
+3)^(1/2))/(-10*x^2-x+3)^(1/2)

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maxima [A]  time = 1.40, size = 116, normalized size = 0.67 \[ -\frac {27}{70} \, {\left (-10 \, x^{2} - x + 3\right )}^{\frac {5}{2}} x^{2} - \frac {2439}{2800} \, {\left (-10 \, x^{2} - x + 3\right )}^{\frac {5}{2}} x - \frac {197487}{280000} \, {\left (-10 \, x^{2} - x + 3\right )}^{\frac {5}{2}} + \frac {141599}{64000} \, {\left (-10 \, x^{2} - x + 3\right )}^{\frac {3}{2}} x + \frac {141599}{1280000} \, {\left (-10 \, x^{2} - x + 3\right )}^{\frac {3}{2}} + \frac {51400437}{5120000} \, \sqrt {-10 \, x^{2} - x + 3} x - \frac {6219452877}{2048000000} \, \sqrt {10} \arcsin \left (-\frac {20}{11} \, x - \frac {1}{11}\right ) + \frac {51400437}{102400000} \, \sqrt {-10 \, x^{2} - x + 3} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(3/2),x, algorithm="maxima")

[Out]

-27/70*(-10*x^2 - x + 3)^(5/2)*x^2 - 2439/2800*(-10*x^2 - x + 3)^(5/2)*x - 197487/280000*(-10*x^2 - x + 3)^(5/
2) + 141599/64000*(-10*x^2 - x + 3)^(3/2)*x + 141599/1280000*(-10*x^2 - x + 3)^(3/2) + 51400437/5120000*sqrt(-
10*x^2 - x + 3)*x - 6219452877/2048000000*sqrt(10)*arcsin(-20/11*x - 1/11) + 51400437/102400000*sqrt(-10*x^2 -
x + 3)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.01 \[ \int {\left (1-2\,x\right )}^{3/2}\,{\left (3\,x+2\right )}^3\,{\left (5\,x+3\right )}^{3/2} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1 - 2*x)^(3/2)*(3*x + 2)^3*(5*x + 3)^(3/2),x)

[Out]

int((1 - 2*x)^(3/2)*(3*x + 2)^3*(5*x + 3)^(3/2), x)

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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((1-2*x)**(3/2)*(2+3*x)**3*(3+5*x)**(3/2),x)

[Out]

Timed out

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