3.25.14 \(\int (1-2 x)^{5/2} (3+5 x)^{5/2} \, dx\) [2414]

Optimal. Leaf size=160 \[ \frac {161051 \sqrt {1-2 x} \sqrt {3+5 x}}{102400}+\frac {14641 (1-2 x)^{3/2} \sqrt {3+5 x}}{30720}+\frac {1331 (1-2 x)^{5/2} \sqrt {3+5 x}}{7680}-\frac {121}{256} (1-2 x)^{7/2} \sqrt {3+5 x}-\frac {11}{48} (1-2 x)^{7/2} (3+5 x)^{3/2}-\frac {1}{12} (1-2 x)^{7/2} (3+5 x)^{5/2}+\frac {1771561 \sin ^{-1}\left (\sqrt {\frac {2}{11}} \sqrt {3+5 x}\right )}{102400 \sqrt {10}} \]

[Out]

-11/48*(1-2*x)^(7/2)*(3+5*x)^(3/2)-1/12*(1-2*x)^(7/2)*(3+5*x)^(5/2)+1771561/1024000*arcsin(1/11*22^(1/2)*(3+5*
x)^(1/2))*10^(1/2)+14641/30720*(1-2*x)^(3/2)*(3+5*x)^(1/2)+1331/7680*(1-2*x)^(5/2)*(3+5*x)^(1/2)-121/256*(1-2*
x)^(7/2)*(3+5*x)^(1/2)+161051/102400*(1-2*x)^(1/2)*(3+5*x)^(1/2)

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Rubi [A]
time = 0.03, antiderivative size = 160, normalized size of antiderivative = 1.00, number of steps used = 8, number of rules used = 3, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.158, Rules used = {52, 56, 222} \begin {gather*} \frac {1771561 \text {ArcSin}\left (\sqrt {\frac {2}{11}} \sqrt {5 x+3}\right )}{102400 \sqrt {10}}-\frac {1}{12} (5 x+3)^{5/2} (1-2 x)^{7/2}-\frac {11}{48} (5 x+3)^{3/2} (1-2 x)^{7/2}-\frac {121}{256} \sqrt {5 x+3} (1-2 x)^{7/2}+\frac {1331 \sqrt {5 x+3} (1-2 x)^{5/2}}{7680}+\frac {14641 \sqrt {5 x+3} (1-2 x)^{3/2}}{30720}+\frac {161051 \sqrt {5 x+3} \sqrt {1-2 x}}{102400} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(161051*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/102400 + (14641*(1 - 2*x)^(3/2)*Sqrt[3 + 5*x])/30720 + (1331*(1 - 2*x)^(5
/2)*Sqrt[3 + 5*x])/7680 - (121*(1 - 2*x)^(7/2)*Sqrt[3 + 5*x])/256 - (11*(1 - 2*x)^(7/2)*(3 + 5*x)^(3/2))/48 -
((1 - 2*x)^(7/2)*(3 + 5*x)^(5/2))/12 + (1771561*ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]])/(102400*Sqrt[10])

Rule 52

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 56

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 222

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} (3+5 x)^{5/2} \, dx &=-\frac {1}{12} (1-2 x)^{7/2} (3+5 x)^{5/2}+\frac {55}{24} \int (1-2 x)^{5/2} (3+5 x)^{3/2} \, dx\\ &=-\frac {11}{48} (1-2 x)^{7/2} (3+5 x)^{3/2}-\frac {1}{12} (1-2 x)^{7/2} (3+5 x)^{5/2}+\frac {121}{32} \int (1-2 x)^{5/2} \sqrt {3+5 x} \, dx\\ &=-\frac {121}{256} (1-2 x)^{7/2} \sqrt {3+5 x}-\frac {11}{48} (1-2 x)^{7/2} (3+5 x)^{3/2}-\frac {1}{12} (1-2 x)^{7/2} (3+5 x)^{5/2}+\frac {1331}{512} \int \frac {(1-2 x)^{5/2}}{\sqrt {3+5 x}} \, dx\\ &=\frac {1331 (1-2 x)^{5/2} \sqrt {3+5 x}}{7680}-\frac {121}{256} (1-2 x)^{7/2} \sqrt {3+5 x}-\frac {11}{48} (1-2 x)^{7/2} (3+5 x)^{3/2}-\frac {1}{12} (1-2 x)^{7/2} (3+5 x)^{5/2}+\frac {14641 \int \frac {(1-2 x)^{3/2}}{\sqrt {3+5 x}} \, dx}{3072}\\ &=\frac {14641 (1-2 x)^{3/2} \sqrt {3+5 x}}{30720}+\frac {1331 (1-2 x)^{5/2} \sqrt {3+5 x}}{7680}-\frac {121}{256} (1-2 x)^{7/2} \sqrt {3+5 x}-\frac {11}{48} (1-2 x)^{7/2} (3+5 x)^{3/2}-\frac {1}{12} (1-2 x)^{7/2} (3+5 x)^{5/2}+\frac {161051 \int \frac {\sqrt {1-2 x}}{\sqrt {3+5 x}} \, dx}{20480}\\ &=\frac {161051 \sqrt {1-2 x} \sqrt {3+5 x}}{102400}+\frac {14641 (1-2 x)^{3/2} \sqrt {3+5 x}}{30720}+\frac {1331 (1-2 x)^{5/2} \sqrt {3+5 x}}{7680}-\frac {121}{256} (1-2 x)^{7/2} \sqrt {3+5 x}-\frac {11}{48} (1-2 x)^{7/2} (3+5 x)^{3/2}-\frac {1}{12} (1-2 x)^{7/2} (3+5 x)^{5/2}+\frac {1771561 \int \frac {1}{\sqrt {1-2 x} \sqrt {3+5 x}} \, dx}{204800}\\ &=\frac {161051 \sqrt {1-2 x} \sqrt {3+5 x}}{102400}+\frac {14641 (1-2 x)^{3/2} \sqrt {3+5 x}}{30720}+\frac {1331 (1-2 x)^{5/2} \sqrt {3+5 x}}{7680}-\frac {121}{256} (1-2 x)^{7/2} \sqrt {3+5 x}-\frac {11}{48} (1-2 x)^{7/2} (3+5 x)^{3/2}-\frac {1}{12} (1-2 x)^{7/2} (3+5 x)^{5/2}+\frac {1771561 \text {Subst}\left (\int \frac {1}{\sqrt {11-2 x^2}} \, dx,x,\sqrt {3+5 x}\right )}{102400 \sqrt {5}}\\ &=\frac {161051 \sqrt {1-2 x} \sqrt {3+5 x}}{102400}+\frac {14641 (1-2 x)^{3/2} \sqrt {3+5 x}}{30720}+\frac {1331 (1-2 x)^{5/2} \sqrt {3+5 x}}{7680}-\frac {121}{256} (1-2 x)^{7/2} \sqrt {3+5 x}-\frac {11}{48} (1-2 x)^{7/2} (3+5 x)^{3/2}-\frac {1}{12} (1-2 x)^{7/2} (3+5 x)^{5/2}+\frac {1771561 \sin ^{-1}\left (\sqrt {\frac {2}{11}} \sqrt {3+5 x}\right )}{102400 \sqrt {10}}\\ \end {align*}

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Mathematica [A]
time = 0.22, size = 88, normalized size = 0.55 \begin {gather*} \frac {10 \sqrt {1-2 x} \left (288009+6165075 x+7229180 x^2-18460000 x^3-20688000 x^4+21760000 x^5+25600000 x^6\right )-5314683 \sqrt {30+50 x} \tan ^{-1}\left (\frac {\sqrt {\frac {5}{2}-5 x}}{\sqrt {3+5 x}}\right )}{3072000 \sqrt {3+5 x}} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(10*Sqrt[1 - 2*x]*(288009 + 6165075*x + 7229180*x^2 - 18460000*x^3 - 20688000*x^4 + 21760000*x^5 + 25600000*x^
6) - 5314683*Sqrt[30 + 50*x]*ArcTan[Sqrt[5/2 - 5*x]/Sqrt[3 + 5*x]])/(3072000*Sqrt[3 + 5*x])

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Maple [A]
time = 0.12, size = 136, normalized size = 0.85

method	result	size
risch	\(-\frac {\left (5120000 x^{5}+1280000 x^{4}-4905600 x^{3}-748640 x^{2}+1895020 x +96003\right ) \sqrt {3+5 x}\, \left (-1+2 x \right ) \sqrt {\left (1-2 x \right ) \left (3+5 x \right )}}{307200 \sqrt {-\left (3+5 x \right ) \left (-1+2 x \right )}\, \sqrt {1-2 x}}+\frac {1771561 \sqrt {10}\, \arcsin \left (\frac {20 x}{11}+\frac {1}{11}\right ) \sqrt {\left (1-2 x \right ) \left (3+5 x \right )}}{2048000 \sqrt {1-2 x}\, \sqrt {3+5 x}}\)	\(113\)
default	\(\frac {\left (1-2 x \right )^{\frac {5}{2}} \left (3+5 x \right )^{\frac {7}{2}}}{30}+\frac {11 \left (1-2 x \right )^{\frac {3}{2}} \left (3+5 x \right )^{\frac {7}{2}}}{300}+\frac {121 \left (3+5 x \right )^{\frac {7}{2}} \sqrt {1-2 x}}{4000}-\frac {1331 \left (3+5 x \right )^{\frac {5}{2}} \sqrt {1-2 x}}{48000}-\frac {14641 \left (3+5 x \right )^{\frac {3}{2}} \sqrt {1-2 x}}{76800}-\frac {161051 \sqrt {1-2 x}\, \sqrt {3+5 x}}{102400}+\frac {1771561 \sqrt {10}\, \arcsin \left (\frac {20 x}{11}+\frac {1}{11}\right ) \sqrt {\left (1-2 x \right ) \left (3+5 x \right )}}{2048000 \sqrt {1-2 x}\, \sqrt {3+5 x}}\)	\(136\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/30*(1-2*x)^(5/2)*(3+5*x)^(7/2)+11/300*(1-2*x)^(3/2)*(3+5*x)^(7/2)+121/4000*(3+5*x)^(7/2)*(1-2*x)^(1/2)-1331/
48000*(3+5*x)^(5/2)*(1-2*x)^(1/2)-14641/76800*(3+5*x)^(3/2)*(1-2*x)^(1/2)-161051/102400*(1-2*x)^(1/2)*(3+5*x)^
(1/2)+1771561/2048000*10^(1/2)*arcsin(20/11*x+1/11)*((1-2*x)*(3+5*x))^(1/2)/(1-2*x)^(1/2)/(3+5*x)^(1/2)

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Maxima [A]
time = 0.50, size = 99, normalized size = 0.62 \begin {gather*} \frac {1}{6} \, {\left (-10 \, x^{2} - x + 3\right )}^{\frac {5}{2}} x + \frac {1}{120} \, {\left (-10 \, x^{2} - x + 3\right )}^{\frac {5}{2}} + \frac {121}{192} \, {\left (-10 \, x^{2} - x + 3\right )}^{\frac {3}{2}} x + \frac {121}{3840} \, {\left (-10 \, x^{2} - x + 3\right )}^{\frac {3}{2}} + \frac {14641}{5120} \, \sqrt {-10 \, x^{2} - x + 3} x - \frac {1771561}{2048000} \, \sqrt {10} \arcsin \left (-\frac {20}{11} \, x - \frac {1}{11}\right ) + \frac {14641}{102400} \, \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)*(3+5*x)^(5/2),x, algorithm="maxima")

[Out]

1/6*(-10*x^2 - x + 3)^(5/2)*x + 1/120*(-10*x^2 - x + 3)^(5/2) + 121/192*(-10*x^2 - x + 3)^(3/2)*x + 121/3840*(
-10*x^2 - x + 3)^(3/2) + 14641/5120*sqrt(-10*x^2 - x + 3)*x - 1771561/2048000*sqrt(10)*arcsin(-20/11*x - 1/11)
+ 14641/102400*sqrt(-10*x^2 - x + 3)

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Fricas [A]
time = 0.57, size = 82, normalized size = 0.51 \begin {gather*} \frac {1}{307200} \, {\left (5120000 \, x^{5} + 1280000 \, x^{4} - 4905600 \, x^{3} - 748640 \, x^{2} + 1895020 \, x + 96003\right )} \sqrt {5 \, x + 3} \sqrt {-2 \, x + 1} - \frac {1771561}{2048000} \, \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)*(3+5*x)^(5/2),x, algorithm="fricas")

[Out]

1/307200*(5120000*x^5 + 1280000*x^4 - 4905600*x^3 - 748640*x^2 + 1895020*x + 96003)*sqrt(5*x + 3)*sqrt(-2*x +
1) - 1771561/2048000*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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Sympy [C] Result contains complex when optimal does not.
time = 194.55, size = 355, normalized size = 2.22 \begin {gather*} \begin {cases} \frac {500 i \left (x + \frac {3}{5}\right )^{\frac {13}{2}}}{3 \sqrt {10 x - 5}} - \frac {1925 i \left (x + \frac {3}{5}\right )^{\frac {11}{2}}}{3 \sqrt {10 x - 5}} + \frac {40535 i \left (x + \frac {3}{5}\right )^{\frac {9}{2}}}{48 \sqrt {10 x - 5}} - \frac {73205 i \left (x + \frac {3}{5}\right )^{\frac {7}{2}}}{192 \sqrt {10 x - 5}} - \frac {14641 i \left (x + \frac {3}{5}\right )^{\frac {5}{2}}}{7680 \sqrt {10 x - 5}} - \frac {161051 i \left (x + \frac {3}{5}\right )^{\frac {3}{2}}}{30720 \sqrt {10 x - 5}} + \frac {1771561 i \sqrt {x + \frac {3}{5}}}{102400 \sqrt {10 x - 5}} - \frac {1771561 \sqrt {10} i \operatorname {acosh}{\left (\frac {\sqrt {110} \sqrt {x + \frac {3}{5}}}{11} \right )}}{1024000} & \text {for}\: \left |{x + \frac {3}{5}}\right | > \frac {11}{10} \\\frac {1771561 \sqrt {10} \operatorname {asin}{\left (\frac {\sqrt {110} \sqrt {x + \frac {3}{5}}}{11} \right )}}{1024000} - \frac {500 \left (x + \frac {3}{5}\right )^{\frac {13}{2}}}{3 \sqrt {5 - 10 x}} + \frac {1925 \left (x + \frac {3}{5}\right )^{\frac {11}{2}}}{3 \sqrt {5 - 10 x}} - \frac {40535 \left (x + \frac {3}{5}\right )^{\frac {9}{2}}}{48 \sqrt {5 - 10 x}} + \frac {73205 \left (x + \frac {3}{5}\right )^{\frac {7}{2}}}{192 \sqrt {5 - 10 x}} + \frac {14641 \left (x + \frac {3}{5}\right )^{\frac {5}{2}}}{7680 \sqrt {5 - 10 x}} + \frac {161051 \left (x + \frac {3}{5}\right )^{\frac {3}{2}}}{30720 \sqrt {5 - 10 x}} - \frac {1771561 \sqrt {x + \frac {3}{5}}}{102400 \sqrt {5 - 10 x}} & \text {otherwise} \end {cases} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

Piecewise((500*I*(x + 3/5)**(13/2)/(3*sqrt(10*x - 5)) - 1925*I*(x + 3/5)**(11/2)/(3*sqrt(10*x - 5)) + 40535*I*
(x + 3/5)**(9/2)/(48*sqrt(10*x - 5)) - 73205*I*(x + 3/5)**(7/2)/(192*sqrt(10*x - 5)) - 14641*I*(x + 3/5)**(5/2
)/(7680*sqrt(10*x - 5)) - 161051*I*(x + 3/5)**(3/2)/(30720*sqrt(10*x - 5)) + 1771561*I*sqrt(x + 3/5)/(102400*s
qrt(10*x - 5)) - 1771561*sqrt(10)*I*acosh(sqrt(110)*sqrt(x + 3/5)/11)/1024000, Abs(x + 3/5) > 11/10), (1771561
*sqrt(10)*asin(sqrt(110)*sqrt(x + 3/5)/11)/1024000 - 500*(x + 3/5)**(13/2)/(3*sqrt(5 - 10*x)) + 1925*(x + 3/5)
**(11/2)/(3*sqrt(5 - 10*x)) - 40535*(x + 3/5)**(9/2)/(48*sqrt(5 - 10*x)) + 73205*(x + 3/5)**(7/2)/(192*sqrt(5
- 10*x)) + 14641*(x + 3/5)**(5/2)/(7680*sqrt(5 - 10*x)) + 161051*(x + 3/5)**(3/2)/(30720*sqrt(5 - 10*x)) - 177
1561*sqrt(x + 3/5)/(102400*sqrt(5 - 10*x)), True))

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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 356 vs. \(2 (115) = 230\).
time = 0.85, size = 356, normalized size = 2.22 \begin {gather*} \frac {1}{76800000} \, \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 {1}{2400000} \, \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 {47}{1920000} \, \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 {69}{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}{2000} \, \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}{50} \, \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)*(3+5*x)^(5/2),x, algorithm="giac")

[Out]

1/76800000*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))) +
1/2400000*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))) - 47/1920000*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))) - 69/40000*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))) + 27/2000*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))) + 27/50*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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Mupad [F]
time = 0.00, size = -1, normalized size = -0.01 \begin {gather*} \int {\left (1-2\,x\right )}^{5/2}\,{\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)*(5*x + 3)^(5/2),x)

[Out]

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

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