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

Optimal. Leaf size=182 \[ -\frac {3}{70} (5 x+3)^{7/2} (1-2 x)^{7/2}-\frac {37}{240} (5 x+3)^{5/2} (1-2 x)^{7/2}-\frac {407}{960} (5 x+3)^{3/2} (1-2 x)^{7/2}-\frac {4477 \sqrt {5 x+3} (1-2 x)^{7/2}}{5120}+\frac {49247 \sqrt {5 x+3} (1-2 x)^{5/2}}{153600}+\frac {541717 \sqrt {5 x+3} (1-2 x)^{3/2}}{614400}+\frac {5958887 \sqrt {5 x+3} \sqrt {1-2 x}}{2048000}+\frac {65547757 \sin ^{-1}\left (\sqrt {\frac {2}{11}} \sqrt {5 x+3}\right )}{2048000 \sqrt {10}} \]

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Rubi [A]  time = 0.06, antiderivative size = 182, normalized size of antiderivative = 1.00, number of steps used = 9, number of rules used = 4, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {80, 50, 54, 216} \begin {gather*} -\frac {3}{70} (5 x+3)^{7/2} (1-2 x)^{7/2}-\frac {37}{240} (5 x+3)^{5/2} (1-2 x)^{7/2}-\frac {407}{960} (5 x+3)^{3/2} (1-2 x)^{7/2}-\frac {4477 \sqrt {5 x+3} (1-2 x)^{7/2}}{5120}+\frac {49247 \sqrt {5 x+3} (1-2 x)^{5/2}}{153600}+\frac {541717 \sqrt {5 x+3} (1-2 x)^{3/2}}{614400}+\frac {5958887 \sqrt {5 x+3} \sqrt {1-2 x}}{2048000}+\frac {65547757 \sin ^{-1}\left (\sqrt {\frac {2}{11}} \sqrt {5 x+3}\right )}{2048000 \sqrt {10}} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(5958887*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/2048000 + (541717*(1 - 2*x)^(3/2)*Sqrt[3 + 5*x])/614400 + (49247*(1 - 2*
x)^(5/2)*Sqrt[3 + 5*x])/153600 - (4477*(1 - 2*x)^(7/2)*Sqrt[3 + 5*x])/5120 - (407*(1 - 2*x)^(7/2)*(3 + 5*x)^(3
/2))/960 - (37*(1 - 2*x)^(7/2)*(3 + 5*x)^(5/2))/240 - (3*(1 - 2*x)^(7/2)*(3 + 5*x)^(7/2))/70 + (65547757*ArcSi
n[Sqrt[2/11]*Sqrt[3 + 5*x]])/(2048000*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 80

Int[((a_.) + (b_.)*(x_))*((c_.) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Simp[(b*(c + d*x)
^(n + 1)*(e + f*x)^(p + 1))/(d*f*(n + p + 2)), x] + Dist[(a*d*f*(n + p + 2) - b*(d*e*(n + 1) + c*f*(p + 1)))/(
d*f*(n + p + 2)), Int[(c + d*x)^n*(e + f*x)^p, x], x] /; FreeQ[{a, b, c, d, e, f, n, p}, x] && NeQ[n + p + 2,
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)^{5/2} (2+3 x) (3+5 x)^{5/2} \, dx &=-\frac {3}{70} (1-2 x)^{7/2} (3+5 x)^{7/2}+\frac {37}{20} \int (1-2 x)^{5/2} (3+5 x)^{5/2} \, dx\\ &=-\frac {37}{240} (1-2 x)^{7/2} (3+5 x)^{5/2}-\frac {3}{70} (1-2 x)^{7/2} (3+5 x)^{7/2}+\frac {407}{96} \int (1-2 x)^{5/2} (3+5 x)^{3/2} \, dx\\ &=-\frac {407}{960} (1-2 x)^{7/2} (3+5 x)^{3/2}-\frac {37}{240} (1-2 x)^{7/2} (3+5 x)^{5/2}-\frac {3}{70} (1-2 x)^{7/2} (3+5 x)^{7/2}+\frac {4477}{640} \int (1-2 x)^{5/2} \sqrt {3+5 x} \, dx\\ &=-\frac {4477 (1-2 x)^{7/2} \sqrt {3+5 x}}{5120}-\frac {407}{960} (1-2 x)^{7/2} (3+5 x)^{3/2}-\frac {37}{240} (1-2 x)^{7/2} (3+5 x)^{5/2}-\frac {3}{70} (1-2 x)^{7/2} (3+5 x)^{7/2}+\frac {49247 \int \frac {(1-2 x)^{5/2}}{\sqrt {3+5 x}} \, dx}{10240}\\ &=\frac {49247 (1-2 x)^{5/2} \sqrt {3+5 x}}{153600}-\frac {4477 (1-2 x)^{7/2} \sqrt {3+5 x}}{5120}-\frac {407}{960} (1-2 x)^{7/2} (3+5 x)^{3/2}-\frac {37}{240} (1-2 x)^{7/2} (3+5 x)^{5/2}-\frac {3}{70} (1-2 x)^{7/2} (3+5 x)^{7/2}+\frac {541717 \int \frac {(1-2 x)^{3/2}}{\sqrt {3+5 x}} \, dx}{61440}\\ &=\frac {541717 (1-2 x)^{3/2} \sqrt {3+5 x}}{614400}+\frac {49247 (1-2 x)^{5/2} \sqrt {3+5 x}}{153600}-\frac {4477 (1-2 x)^{7/2} \sqrt {3+5 x}}{5120}-\frac {407}{960} (1-2 x)^{7/2} (3+5 x)^{3/2}-\frac {37}{240} (1-2 x)^{7/2} (3+5 x)^{5/2}-\frac {3}{70} (1-2 x)^{7/2} (3+5 x)^{7/2}+\frac {5958887 \int \frac {\sqrt {1-2 x}}{\sqrt {3+5 x}} \, dx}{409600}\\ &=\frac {5958887 \sqrt {1-2 x} \sqrt {3+5 x}}{2048000}+\frac {541717 (1-2 x)^{3/2} \sqrt {3+5 x}}{614400}+\frac {49247 (1-2 x)^{5/2} \sqrt {3+5 x}}{153600}-\frac {4477 (1-2 x)^{7/2} \sqrt {3+5 x}}{5120}-\frac {407}{960} (1-2 x)^{7/2} (3+5 x)^{3/2}-\frac {37}{240} (1-2 x)^{7/2} (3+5 x)^{5/2}-\frac {3}{70} (1-2 x)^{7/2} (3+5 x)^{7/2}+\frac {65547757 \int \frac {1}{\sqrt {1-2 x} \sqrt {3+5 x}} \, dx}{4096000}\\ &=\frac {5958887 \sqrt {1-2 x} \sqrt {3+5 x}}{2048000}+\frac {541717 (1-2 x)^{3/2} \sqrt {3+5 x}}{614400}+\frac {49247 (1-2 x)^{5/2} \sqrt {3+5 x}}{153600}-\frac {4477 (1-2 x)^{7/2} \sqrt {3+5 x}}{5120}-\frac {407}{960} (1-2 x)^{7/2} (3+5 x)^{3/2}-\frac {37}{240} (1-2 x)^{7/2} (3+5 x)^{5/2}-\frac {3}{70} (1-2 x)^{7/2} (3+5 x)^{7/2}+\frac {65547757 \operatorname {Subst}\left (\int \frac {1}{\sqrt {11-2 x^2}} \, dx,x,\sqrt {3+5 x}\right )}{2048000 \sqrt {5}}\\ &=\frac {5958887 \sqrt {1-2 x} \sqrt {3+5 x}}{2048000}+\frac {541717 (1-2 x)^{3/2} \sqrt {3+5 x}}{614400}+\frac {49247 (1-2 x)^{5/2} \sqrt {3+5 x}}{153600}-\frac {4477 (1-2 x)^{7/2} \sqrt {3+5 x}}{5120}-\frac {407}{960} (1-2 x)^{7/2} (3+5 x)^{3/2}-\frac {37}{240} (1-2 x)^{7/2} (3+5 x)^{5/2}-\frac {3}{70} (1-2 x)^{7/2} (3+5 x)^{7/2}+\frac {65547757 \sin ^{-1}\left (\sqrt {\frac {2}{11}} \sqrt {3+5 x}\right )}{2048000 \sqrt {10}}\\ \end {align*}

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Mathematica [A]  time = 0.10, size = 89, normalized size = 0.49 \begin {gather*} \frac {1376502897 \sqrt {20 x-10} \sinh ^{-1}\left (\sqrt {\frac {5}{11}} \sqrt {2 x-1}\right )-10 \sqrt {5 x+3} \left (3686400000 x^7+1914880000 x^6-4423168000 x^5-1928902400 x^4+2174838080 x^3+793975720 x^2-590379826 x+24901623\right )}{430080000 \sqrt {1-2 x}} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(-10*Sqrt[3 + 5*x]*(24901623 - 590379826*x + 793975720*x^2 + 2174838080*x^3 - 1928902400*x^4 - 4423168000*x^5
+ 1914880000*x^6 + 3686400000*x^7) + 1376502897*Sqrt[-10 + 20*x]*ArcSinh[Sqrt[5/11]*Sqrt[-1 + 2*x]])/(43008000
0*Sqrt[1 - 2*x])

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IntegrateAlgebraic [A]  time = 0.30, size = 173, normalized size = 0.95 \begin {gather*} -\frac {1771561 \sqrt {1-2 x} \left (\frac {12140625 (1-2 x)^6}{(5 x+3)^6}+\frac {32375000 (1-2 x)^5}{(5 x+3)^5}+\frac {36648500 (1-2 x)^4}{(5 x+3)^4}+\frac {20275200 (1-2 x)^3}{(5 x+3)^3}-\frac {5863760 (1-2 x)^2}{(5 x+3)^2}-\frac {828800 (1-2 x)}{5 x+3}-49728\right )}{43008000 \sqrt {5 x+3} \left (\frac {5 (1-2 x)}{5 x+3}+2\right )^7}-\frac {65547757 \tan ^{-1}\left (\frac {\sqrt {\frac {5}{2}} \sqrt {1-2 x}}{\sqrt {5 x+3}}\right )}{2048000 \sqrt {10}} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(-1771561*Sqrt[1 - 2*x]*(-49728 + (12140625*(1 - 2*x)^6)/(3 + 5*x)^6 + (32375000*(1 - 2*x)^5)/(3 + 5*x)^5 + (3
6648500*(1 - 2*x)^4)/(3 + 5*x)^4 + (20275200*(1 - 2*x)^3)/(3 + 5*x)^3 - (5863760*(1 - 2*x)^2)/(3 + 5*x)^2 - (8
28800*(1 - 2*x))/(3 + 5*x)))/(43008000*Sqrt[3 + 5*x]*(2 + (5*(1 - 2*x))/(3 + 5*x))^7) - (65547757*ArcTan[(Sqrt
[5/2]*Sqrt[1 - 2*x])/Sqrt[3 + 5*x]])/(2048000*Sqrt[10])

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fricas [A]  time = 1.36, size = 87, normalized size = 0.48 \begin {gather*} \frac {1}{43008000} \, {\left (1843200000 \, x^{6} + 1879040000 \, x^{5} - 1272064000 \, x^{4} - 1600483200 \, x^{3} + 287177440 \, x^{2} + 540576580 \, x - 24901623\right )} \sqrt {5 \, x + 3} \sqrt {-2 \, x + 1} - \frac {65547757}{40960000} \, \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 ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/43008000*(1843200000*x^6 + 1879040000*x^5 - 1272064000*x^4 - 1600483200*x^3 + 287177440*x^2 + 540576580*x -
24901623)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 65547757/40960000*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 = 1.79, size = 446, normalized size = 2.45 \begin {gather*} \frac {1}{3584000000} \, \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 {11}{192000000} \, \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 {19}{192000000} \, \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 {1091}{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 {111}{40000} \, \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 {27}{400} \, \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 {27}{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 )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/3584000000*sqrt(5)*(2*(4*(8*(4*(16*(20*(120*x - 443)*(5*x + 3) + 94933)*(5*x + 3) - 7838433)*(5*x + 3) + 987
94353)*(5*x + 3) - 1568443065)*(5*x + 3) + 8438816295)*sqrt(5*x + 3)*sqrt(-10*x + 5) + 17534989395*sqrt(2)*arc
sin(1/11*sqrt(22)*sqrt(5*x + 3))) + 11/192000000*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))) + 19/192000000*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))) - 1091/9600000*sqrt(5)*(2*(4*(8*(60*x - 119)*(5*x + 3) + 6163)*(5*x + 3) - 66189)*sqrt(5*x + 3)*sq
rt(-10*x + 5) - 184305*sqrt(2)*arcsin(1/11*sqrt(22)*sqrt(5*x + 3))) - 111/40000*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))) + 27/400*sqrt(
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))) + 27/25*sqr
t(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 = 0.85 \begin {gather*} \frac {\sqrt {-2 x +1}\, \sqrt {5 x +3}\, \left (36864000000 \sqrt {-10 x^{2}-x +3}\, x^{6}[phone] \sqrt {-10 x^{2}-x +3}\, x^{5}-25441280000 \sqrt {-10 x^{2}-x +3}\, x^{4}-32009664000 \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 )-498032460 \sqrt {-10 x^{2}-x +3}\right )}{860160000 \sqrt {-10 x^{2}-x +3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/860160000*(-2*x+1)^(1/2)*(5*x+3)^(1/2)*(36864000000*(-10*x^2-x+3)^(1/2)*x^6+37580800000*(-10*x^2-x+3)^(1/2)*
x^5-25441280000*(-10*x^2-x+3)^(1/2)*x^4-32009664000*(-10*x^2-x+3)^(1/2)*x^3+5743548800*(-10*x^2-x+3)^(1/2)*x^2
[phone]*10^(1/2)*arcsin(20/11*x+1/11)[phone]*(-10*x^2-x+3)^(1/2)*x-498032460*(-10*x^2-x+3)^(1/2))/(-1
0*x^2-x+3)^(1/2)

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maxima [A]  time = 1.22, size = 113, normalized size = 0.62 \begin {gather*} -\frac {3}{70} \, {\left (-10 \, x^{2} - x + 3\right )}^{\frac {7}{2}} + \frac {37}{120} \, {\left (-10 \, x^{2} - x + 3\right )}^{\frac {5}{2}} x + \frac {37}{2400} \, {\left (-10 \, x^{2} - x + 3\right )}^{\frac {5}{2}} + \frac {4477}{3840} \, {\left (-10 \, x^{2} - x + 3\right )}^{\frac {3}{2}} x + \frac {4477}{76800} \, {\left (-10 \, x^{2} - x + 3\right )}^{\frac {3}{2}} + \frac {541717}{102400} \, \sqrt {-10 \, x^{2} - x + 3} x - \frac {65547757}{40960000} \, \sqrt {10} \arcsin \left (-\frac {20}{11} \, x - \frac {1}{11}\right ) + \frac {541717}{2048000} \, \sqrt {-10 \, x^{2} - x + 3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-3/70*(-10*x^2 - x + 3)^(7/2) + 37/120*(-10*x^2 - x + 3)^(5/2)*x + 37/2400*(-10*x^2 - x + 3)^(5/2) + 4477/3840
*(-10*x^2 - x + 3)^(3/2)*x + 4477/76800*(-10*x^2 - x + 3)^(3/2) + 541717/102400*sqrt(-10*x^2 - x + 3)*x - 6554
7757/40960000*sqrt(10)*arcsin(-20/11*x - 1/11) + 541717/2048000*sqrt(-10*x^2 - x + 3)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

[Out]

Timed out

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