3.2274 \(\int \sqrt{1-2 x} (2+3 x)^4 (3+5 x)^{3/2} \, dx\)
Optimal. Leaf size=179 \[ -\frac{3}{70} (1-2 x)^{3/2} (5 x+3)^{5/2} (3 x+2)^3-\frac{403 (1-2 x)^{3/2} (5 x+3)^{5/2} (3 x+2)^2}{2800}-\frac{52760369 (1-2 x)^{3/2} (5 x+3)^{3/2}}{7680000}-\frac{(1-2 x)^{3/2} (5 x+3)^{5/2} (874608 x+1480103)}{640000}-\frac{580364059 (1-2 x)^{3/2} \sqrt{5 x+3}}{20480000}+\frac{6384004649 \sqrt{1-2 x} \sqrt{5 x+3}}{204800000}+\frac{70224051139 \sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )}{204800000 \sqrt{10}} \]
[Out]
(6384004649*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/204800000 - (580364059*(1 - 2*x)^(3/2)*Sqrt[3 + 5*x])/20480000 - (527
60369*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/7680000 - (403*(1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^(5/2))/2800 - (3*(
1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x)^(5/2))/70 - ((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)*(1480103 + 874608*x))/640000
+ (70224051139*ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]])/(204800000*Sqrt[10])
________________________________________________________________________________________
Rubi [A] time = 0.0566364, antiderivative size = 179, normalized size of antiderivative = 1.,
number of steps used = 8, number of rules used = 6, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231, Rules used =
{100, 153, 147, 50, 54, 216} \[ -\frac{3}{70} (1-2 x)^{3/2} (5 x+3)^{5/2} (3 x+2)^3-\frac{403 (1-2 x)^{3/2} (5 x+3)^{5/2} (3 x+2)^2}{2800}-\frac{52760369 (1-2 x)^{3/2} (5 x+3)^{3/2}}{7680000}-\frac{(1-2 x)^{3/2} (5 x+3)^{5/2} (874608 x+1480103)}{640000}-\frac{580364059 (1-2 x)^{3/2} \sqrt{5 x+3}}{20480000}+\frac{6384004649 \sqrt{1-2 x} \sqrt{5 x+3}}{204800000}+\frac{70224051139 \sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )}{204800000 \sqrt{10}} \]
Antiderivative was successfully verified.
[In]
Int[Sqrt[1 - 2*x]*(2 + 3*x)^4*(3 + 5*x)^(3/2),x]
[Out]
(6384004649*Sqrt[1 - 2*x]*Sqrt[3 + 5*x])/204800000 - (580364059*(1 - 2*x)^(3/2)*Sqrt[3 + 5*x])/20480000 - (527
60369*(1 - 2*x)^(3/2)*(3 + 5*x)^(3/2))/7680000 - (403*(1 - 2*x)^(3/2)*(2 + 3*x)^2*(3 + 5*x)^(5/2))/2800 - (3*(
1 - 2*x)^(3/2)*(2 + 3*x)^3*(3 + 5*x)^(5/2))/70 - ((1 - 2*x)^(3/2)*(3 + 5*x)^(5/2)*(1480103 + 874608*x))/640000
+ (70224051139*ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]])/(204800000*Sqrt[10])
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 153
Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_)*((e_.) + (f_.)*(x_))^(p_)*((g_.) + (h_.)*(x_)), x_Symb
ol] :> Simp[(h*(a + b*x)^m*(c + d*x)^(n + 1)*(e + f*x)^(p + 1))/(d*f*(m + n + p + 2)), x] + Dist[1/(d*f*(m + n
+ p + 2)), Int[(a + b*x)^(m - 1)*(c + d*x)^n*(e + f*x)^p*Simp[a*d*f*g*(m + n + p + 2) - h*(b*c*e*m + a*(d*e*(
n + 1) + c*f*(p + 1))) + (b*d*f*g*(m + n + p + 2) + h*(a*d*f*m - b*(d*e*(m + n + 1) + c*f*(m + p + 1))))*x, x]
, x], x] /; FreeQ[{a, b, c, d, e, f, g, h, n, p}, x] && GtQ[m, 0] && NeQ[m + n + p + 2, 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 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 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 \sqrt{1-2 x} (2+3 x)^4 (3+5 x)^{3/2} \, dx &=-\frac{3}{70} (1-2 x)^{3/2} (2+3 x)^3 (3+5 x)^{5/2}-\frac{1}{70} \int \left (-382-\frac{1209 x}{2}\right ) \sqrt{1-2 x} (2+3 x)^2 (3+5 x)^{3/2} \, dx\\ &=-\frac{403 (1-2 x)^{3/2} (2+3 x)^2 (3+5 x)^{5/2}}{2800}-\frac{3}{70} (1-2 x)^{3/2} (2+3 x)^3 (3+5 x)^{5/2}+\frac{\int \sqrt{1-2 x} (2+3 x) (3+5 x)^{3/2} \left (\frac{121905}{2}+\frac{382641 x}{4}\right ) \, dx}{4200}\\ &=-\frac{403 (1-2 x)^{3/2} (2+3 x)^2 (3+5 x)^{5/2}}{2800}-\frac{3}{70} (1-2 x)^{3/2} (2+3 x)^3 (3+5 x)^{5/2}-\frac{(1-2 x)^{3/2} (3+5 x)^{5/2} (1480103+874608 x)}{640000}+\frac{52760369 \int \sqrt{1-2 x} (3+5 x)^{3/2} \, dx}{1280000}\\ &=-\frac{52760369 (1-2 x)^{3/2} (3+5 x)^{3/2}}{7680000}-\frac{403 (1-2 x)^{3/2} (2+3 x)^2 (3+5 x)^{5/2}}{2800}-\frac{3}{70} (1-2 x)^{3/2} (2+3 x)^3 (3+5 x)^{5/2}-\frac{(1-2 x)^{3/2} (3+5 x)^{5/2} (1480103+874608 x)}{640000}+\frac{580364059 \int \sqrt{1-2 x} \sqrt{3+5 x} \, dx}{5120000}\\ &=-\frac{580364059 (1-2 x)^{3/2} \sqrt{3+5 x}}{20480000}-\frac{52760369 (1-2 x)^{3/2} (3+5 x)^{3/2}}{7680000}-\frac{403 (1-2 x)^{3/2} (2+3 x)^2 (3+5 x)^{5/2}}{2800}-\frac{3}{70} (1-2 x)^{3/2} (2+3 x)^3 (3+5 x)^{5/2}-\frac{(1-2 x)^{3/2} (3+5 x)^{5/2} (1480103+874608 x)}{640000}+\frac{6384004649 \int \frac{\sqrt{1-2 x}}{\sqrt{3+5 x}} \, dx}{40960000}\\ &=\frac{6384004649 \sqrt{1-2 x} \sqrt{3+5 x}}{204800000}-\frac{580364059 (1-2 x)^{3/2} \sqrt{3+5 x}}{20480000}-\frac{52760369 (1-2 x)^{3/2} (3+5 x)^{3/2}}{7680000}-\frac{403 (1-2 x)^{3/2} (2+3 x)^2 (3+5 x)^{5/2}}{2800}-\frac{3}{70} (1-2 x)^{3/2} (2+3 x)^3 (3+5 x)^{5/2}-\frac{(1-2 x)^{3/2} (3+5 x)^{5/2} (1480103+874608 x)}{640000}+\frac{70224051139 \int \frac{1}{\sqrt{1-2 x} \sqrt{3+5 x}} \, dx}{409600000}\\ &=\frac{6384004649 \sqrt{1-2 x} \sqrt{3+5 x}}{204800000}-\frac{580364059 (1-2 x)^{3/2} \sqrt{3+5 x}}{20480000}-\frac{52760369 (1-2 x)^{3/2} (3+5 x)^{3/2}}{7680000}-\frac{403 (1-2 x)^{3/2} (2+3 x)^2 (3+5 x)^{5/2}}{2800}-\frac{3}{70} (1-2 x)^{3/2} (2+3 x)^3 (3+5 x)^{5/2}-\frac{(1-2 x)^{3/2} (3+5 x)^{5/2} (1480103+874608 x)}{640000}+\frac{70224051139 \operatorname{Subst}\left (\int \frac{1}{\sqrt{11-2 x^2}} \, dx,x,\sqrt{3+5 x}\right )}{204800000 \sqrt{5}}\\ &=\frac{6384004649 \sqrt{1-2 x} \sqrt{3+5 x}}{204800000}-\frac{580364059 (1-2 x)^{3/2} \sqrt{3+5 x}}{20480000}-\frac{52760369 (1-2 x)^{3/2} (3+5 x)^{3/2}}{7680000}-\frac{403 (1-2 x)^{3/2} (2+3 x)^2 (3+5 x)^{5/2}}{2800}-\frac{3}{70} (1-2 x)^{3/2} (2+3 x)^3 (3+5 x)^{5/2}-\frac{(1-2 x)^{3/2} (3+5 x)^{5/2} (1480103+874608 x)}{640000}+\frac{70224051139 \sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{3+5 x}\right )}{204800000 \sqrt{10}}\\ \end{align*}
Mathematica [A] time = 0.0571696, size = 89, normalized size = 0.5 \[ \frac{-10 \sqrt{5 x+3} \left (497664000000 x^7+1651968000000 x^6+2010963456000 x^5+842711443200 x^4-356020459840 x^3-548703531560 x^2-330110729902 x+201521732121\right )-1474705073919 \sqrt{10-20 x} \sin ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )}{43008000000 \sqrt{1-2 x}} \]
Antiderivative was successfully verified.
[In]
Integrate[Sqrt[1 - 2*x]*(2 + 3*x)^4*(3 + 5*x)^(3/2),x]
[Out]
(-10*Sqrt[3 + 5*x]*(201521732121 - 330110729902*x - 548703531560*x^2 - 356020459840*x^3 + 842711443200*x^4 + 2
010963456000*x^5 + 1651968000000*x^6 + 497664000000*x^7) - 1474705073919*Sqrt[10 - 20*x]*ArcSin[Sqrt[5/11]*Sqr
t[1 - 2*x]])/(43008000000*Sqrt[1 - 2*x])
________________________________________________________________________________________
Maple [A] time = 0.012, size = 155, normalized size = 0.9 \begin{align*}{\frac{1}{86016000000}\sqrt{1-2\,x}\sqrt{3+5\,x} \left ( 4976640000000\,\sqrt{-10\,{x}^{2}-x+3}{x}^{6}+19008000000000\,{x}^{5}\sqrt{-10\,{x}^{2}-x+3}+29613634560000\,{x}^{4}\sqrt{-10\,{x}^{2}-x+3}+23233931712000\,{x}^{3}\sqrt{-10\,{x}^{2}-x+3}+8056761257600\,{x}^{2}\sqrt{-10\,{x}^{2}-x+3}+1474705073919\,\sqrt{10}\arcsin \left ({\frac{20\,x}{11}}+1/11 \right ) -1458654686800\,x\sqrt{-10\,{x}^{2}-x+3}-4030434642420\,\sqrt{-10\,{x}^{2}-x+3} \right ){\frac{1}{\sqrt{-10\,{x}^{2}-x+3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((2+3*x)^4*(3+5*x)^(3/2)*(1-2*x)^(1/2),x)
[Out]
1/86016000000*(1-2*x)^(1/2)*(3+5*x)^(1/2)*(4976640000000*(-10*x^2-x+3)^(1/2)*x^6+19008000000000*x^5*(-10*x^2-x
+3)^(1/2)+29613634560000*x^4*(-10*x^2-x+3)^(1/2)+23233931712000*x^3*(-10*x^2-x+3)^(1/2)+8056761257600*x^2*(-10
*x^2-x+3)^(1/2)+1474705073919*10^(1/2)*arcsin(20/11*x+1/11)-1458654686800*x*(-10*x^2-x+3)^(1/2)-4030434642420*
(-10*x^2-x+3)^(1/2))/(-10*x^2-x+3)^(1/2)
________________________________________________________________________________________
Maxima [A] time = 2.6535, size = 163, normalized size = 0.91 \begin{align*} -\frac{81}{14} \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}} x^{4} - \frac{12051}{560} \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}} x^{3} - \frac{1904661}{56000} \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}} x^{2} - \frac{134695173}{4480000} \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}} x - \frac{890455739}{53760000} \,{\left (-10 \, x^{2} - x + 3\right )}^{\frac{3}{2}} + \frac{580364059}{10240000} \, \sqrt{-10 \, x^{2} - x + 3} x - \frac{70224051139}{4096000000} \, \sqrt{10} \arcsin \left (-\frac{20}{11} \, x - \frac{1}{11}\right ) + \frac{580364059}{204800000} \, \sqrt{-10 \, x^{2} - x + 3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((2+3*x)^4*(3+5*x)^(3/2)*(1-2*x)^(1/2),x, algorithm="maxima")
[Out]
-81/14*(-10*x^2 - x + 3)^(3/2)*x^4 - 12051/560*(-10*x^2 - x + 3)^(3/2)*x^3 - 1904661/56000*(-10*x^2 - x + 3)^(
3/2)*x^2 - 134695173/4480000*(-10*x^2 - x + 3)^(3/2)*x - 890455739/53760000*(-10*x^2 - x + 3)^(3/2) + 58036405
9/10240000*sqrt(-10*x^2 - x + 3)*x - 70224051139/4096000000*sqrt(10)*arcsin(-20/11*x - 1/11) + 580364059/20480
0000*sqrt(-10*x^2 - x + 3)
________________________________________________________________________________________
Fricas [A] time = 1.79654, size = 383, normalized size = 2.14 \begin{align*} \frac{1}{4300800000} \,{\left (248832000000 \, x^{6} + 950400000000 \, x^{5} + 1480681728000 \, x^{4} + 1161696585600 \, x^{3} + 402838062880 \, x^{2} - 72932734340 \, x - 201521732121\right )} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1} - \frac{70224051139}{4096000000} \, \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{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((2+3*x)^4*(3+5*x)^(3/2)*(1-2*x)^(1/2),x, algorithm="fricas")
[Out]
1/4300800000*(248832000000*x^6 + 950400000000*x^5 + 1480681728000*x^4 + 1161696585600*x^3 + 402838062880*x^2 -
72932734340*x - 201521732121)*sqrt(5*x + 3)*sqrt(-2*x + 1) - 70224051139/4096000000*sqrt(10)*arctan(1/20*sqrt
(10)*(20*x + 1)*sqrt(5*x + 3)*sqrt(-2*x + 1)/(10*x^2 + x - 3))
________________________________________________________________________________________
Sympy [A] time = 147.465, size = 925, normalized size = 5.17 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((2+3*x)**4*(3+5*x)**(3/2)*(1-2*x)**(1/2),x)
[Out]
-26411*sqrt(2)*Piecewise((121*sqrt(5)*(-sqrt(5)*sqrt(1 - 2*x)*sqrt(10*x + 6)*(20*x + 1)/121 + asin(sqrt(55)*sq
rt(1 - 2*x)/11))/200, (x <= 1/2) & (x > -3/5)))/64 + 57281*sqrt(2)*Piecewise((1331*sqrt(5)*(-5*sqrt(5)*(1 - 2*
x)**(3/2)*(10*x + 6)**(3/2)/7986 - sqrt(5)*sqrt(1 - 2*x)*sqrt(10*x + 6)*(20*x + 1)/1936 + asin(sqrt(55)*sqrt(1
- 2*x)/11)/16)/125, (x <= 1/2) & (x > -3/5)))/64 - 24843*sqrt(2)*Piecewise((14641*sqrt(5)*(-5*sqrt(5)*(1 - 2*
x)**(3/2)*(10*x + 6)**(3/2)/7986 - sqrt(5)*sqrt(1 - 2*x)*sqrt(10*x + 6)*(20*x + 1)/3872 - sqrt(5)*sqrt(1 - 2*x
)*sqrt(10*x + 6)*(12100*x - 2000*(1 - 2*x)**3 + 6600*(1 - 2*x)**2 - 4719)/1874048 + 5*asin(sqrt(55)*sqrt(1 - 2
*x)/11)/128)/625, (x <= 1/2) & (x > -3/5)))/32 + 10773*sqrt(2)*Piecewise((161051*sqrt(5)*(5*sqrt(5)*(1 - 2*x)*
*(5/2)*(10*x + 6)**(5/2)/322102 - 5*sqrt(5)*(1 - 2*x)**(3/2)*(10*x + 6)**(3/2)/7986 - sqrt(5)*sqrt(1 - 2*x)*sq
rt(10*x + 6)*(20*x + 1)/7744 - 3*sqrt(5)*sqrt(1 - 2*x)*sqrt(10*x + 6)*(12100*x - 2000*(1 - 2*x)**3 + 6600*(1 -
2*x)**2 - 4719)/3748096 + 7*asin(sqrt(55)*sqrt(1 - 2*x)/11)/256)/3125, (x <= 1/2) & (x > -3/5)))/32 - 4671*sq
rt(2)*Piecewise((1771561*sqrt(5)*(5*sqrt(5)*(1 - 2*x)**(5/2)*(10*x + 6)**(5/2)/161051 + 5*sqrt(5)*(1 - 2*x)**(
3/2)*(10*x + 6)**(3/2)*(20*x + 1)**3/170069856 - 5*sqrt(5)*(1 - 2*x)**(3/2)*(10*x + 6)**(3/2)/7986 - sqrt(5)*s
qrt(1 - 2*x)*sqrt(10*x + 6)*(20*x + 1)/15488 - 13*sqrt(5)*sqrt(1 - 2*x)*sqrt(10*x + 6)*(12100*x - 2000*(1 - 2*
x)**3 + 6600*(1 - 2*x)**2 - 4719)/14992384 + 21*asin(sqrt(55)*sqrt(1 - 2*x)/11)/1024)/15625, (x <= 1/2) & (x >
-3/5)))/64 + 405*sqrt(2)*Piecewise((19487171*sqrt(5)*(-125*sqrt(5)*(1 - 2*x)**(7/2)*(10*x + 6)**(7/2)/2728203
94 + 15*sqrt(5)*(1 - 2*x)**(5/2)*(10*x + 6)**(5/2)/322102 + 25*sqrt(5)*(1 - 2*x)**(3/2)*(10*x + 6)**(3/2)*(20*
x + 1)**3/340139712 - 5*sqrt(5)*(1 - 2*x)**(3/2)*(10*x + 6)**(3/2)/7986 - sqrt(5)*sqrt(1 - 2*x)*sqrt(10*x + 6)
*(20*x + 1)/30976 - 25*sqrt(5)*sqrt(1 - 2*x)*sqrt(10*x + 6)*(12100*x - 2000*(1 - 2*x)**3 + 6600*(1 - 2*x)**2 -
4719)/29984768 + 33*asin(sqrt(55)*sqrt(1 - 2*x)/11)/2048)/78125, (x <= 1/2) & (x > -3/5)))/64
________________________________________________________________________________________
Giac [B] time = 1.8619, size = 548, normalized size = 3.06 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((2+3*x)^4*(3+5*x)^(3/2)*(1-2*x)^(1/2),x, algorithm="giac")
[Out]
27/71680000000*sqrt(5)*(2*(4*(8*(4*(16*(20*(120*x - 359)*(5*x + 3) + 63769)*(5*x + 3) - 3968469)*(5*x + 3) + 3
3617829)*(5*x + 3) - 276044685)*(5*x + 3) + 87356115)*sqrt(5*x + 3)*sqrt(-10*x + 5) - 960917265*sqrt(2)*arcsin
(1/11*sqrt(22)*sqrt(5*x + 3))) + 441/2560000000*sqrt(5)*(2*(4*(8*(4*(16*(100*x - 239)*(5*x + 3) + 27999)*(5*x
+ 3) - 318159)*(5*x + 3) + 3237255)*(5*x + 3) - 2656665)*sqrt(5*x + 3)*sqrt(-10*x + 5) + 29223315*sqrt(2)*arcs
in(1/11*sqrt(22)*sqrt(5*x + 3))) + 9/1000000*sqrt(5)*(2*(4*(8*(12*(80*x - 143)*(5*x + 3) + 9773)*(5*x + 3) - 1
36405)*(5*x + 3) + 60555)*sqrt(5*x + 3)*sqrt(-10*x + 5) - 666105*sqrt(2)*arcsin(1/11*sqrt(22)*sqrt(5*x + 3)))
+ 47/80000*sqrt(5)*(2*(4*(8*(60*x - 71)*(5*x + 3) + 2179)*(5*x + 3) - 4125)*sqrt(5*x + 3)*sqrt(-10*x + 5) + 45
375*sqrt(2)*arcsin(1/11*sqrt(22)*sqrt(5*x + 3))) + 23/1500*sqrt(5)*(2*(4*(40*x - 23)*(5*x + 3) + 33)*sqrt(5*x
+ 3)*sqrt(-10*x + 5) - 363*sqrt(2)*arcsin(1/11*sqrt(22)*sqrt(5*x + 3))) + 3/25*sqrt(5)*(2*(20*x + 1)*sqrt(5*x
+ 3)*sqrt(-10*x + 5) + 121*sqrt(2)*arcsin(1/11*sqrt(22)*sqrt(5*x + 3)))