3.2218 \(\int \frac{(a+b x)^{5/2} (A+B x)}{(d+e x)^{19/2}} \, dx\)

Optimal. Leaf size=309 \[ \frac{256 b^4 (a+b x)^{7/2} (-17 a B e+10 A b e+7 b B d)}{765765 e (d+e x)^{7/2} (b d-a e)^6}+\frac{128 b^3 (a+b x)^{7/2} (-17 a B e+10 A b e+7 b B d)}{109395 e (d+e x)^{9/2} (b d-a e)^5}+\frac{32 b^2 (a+b x)^{7/2} (-17 a B e+10 A b e+7 b B d)}{12155 e (d+e x)^{11/2} (b d-a e)^4}+\frac{16 b (a+b x)^{7/2} (-17 a B e+10 A b e+7 b B d)}{3315 e (d+e x)^{13/2} (b d-a e)^3}+\frac{2 (a+b x)^{7/2} (-17 a B e+10 A b e+7 b B d)}{255 e (d+e x)^{15/2} (b d-a e)^2}-\frac{2 (a+b x)^{7/2} (B d-A e)}{17 e (d+e x)^{17/2} (b d-a e)} \]

[Out]

(-2*(B*d - A*e)*(a + b*x)^(7/2))/(17*e*(b*d - a*e)*(d + e*x)^(17/2)) + (2*(7*b*B
*d + 10*A*b*e - 17*a*B*e)*(a + b*x)^(7/2))/(255*e*(b*d - a*e)^2*(d + e*x)^(15/2)
) + (16*b*(7*b*B*d + 10*A*b*e - 17*a*B*e)*(a + b*x)^(7/2))/(3315*e*(b*d - a*e)^3
*(d + e*x)^(13/2)) + (32*b^2*(7*b*B*d + 10*A*b*e - 17*a*B*e)*(a + b*x)^(7/2))/(1
2155*e*(b*d - a*e)^4*(d + e*x)^(11/2)) + (128*b^3*(7*b*B*d + 10*A*b*e - 17*a*B*e
)*(a + b*x)^(7/2))/(109395*e*(b*d - a*e)^5*(d + e*x)^(9/2)) + (256*b^4*(7*b*B*d
+ 10*A*b*e - 17*a*B*e)*(a + b*x)^(7/2))/(765765*e*(b*d - a*e)^6*(d + e*x)^(7/2))

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Rubi [A]  time = 0.584694, antiderivative size = 309, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 3, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ \frac{256 b^4 (a+b x)^{7/2} (-17 a B e+10 A b e+7 b B d)}{765765 e (d+e x)^{7/2} (b d-a e)^6}+\frac{128 b^3 (a+b x)^{7/2} (-17 a B e+10 A b e+7 b B d)}{109395 e (d+e x)^{9/2} (b d-a e)^5}+\frac{32 b^2 (a+b x)^{7/2} (-17 a B e+10 A b e+7 b B d)}{12155 e (d+e x)^{11/2} (b d-a e)^4}+\frac{16 b (a+b x)^{7/2} (-17 a B e+10 A b e+7 b B d)}{3315 e (d+e x)^{13/2} (b d-a e)^3}+\frac{2 (a+b x)^{7/2} (-17 a B e+10 A b e+7 b B d)}{255 e (d+e x)^{15/2} (b d-a e)^2}-\frac{2 (a+b x)^{7/2} (B d-A e)}{17 e (d+e x)^{17/2} (b d-a e)} \]

Antiderivative was successfully verified.

[In]  Int[((a + b*x)^(5/2)*(A + B*x))/(d + e*x)^(19/2),x]

[Out]

(-2*(B*d - A*e)*(a + b*x)^(7/2))/(17*e*(b*d - a*e)*(d + e*x)^(17/2)) + (2*(7*b*B
*d + 10*A*b*e - 17*a*B*e)*(a + b*x)^(7/2))/(255*e*(b*d - a*e)^2*(d + e*x)^(15/2)
) + (16*b*(7*b*B*d + 10*A*b*e - 17*a*B*e)*(a + b*x)^(7/2))/(3315*e*(b*d - a*e)^3
*(d + e*x)^(13/2)) + (32*b^2*(7*b*B*d + 10*A*b*e - 17*a*B*e)*(a + b*x)^(7/2))/(1
2155*e*(b*d - a*e)^4*(d + e*x)^(11/2)) + (128*b^3*(7*b*B*d + 10*A*b*e - 17*a*B*e
)*(a + b*x)^(7/2))/(109395*e*(b*d - a*e)^5*(d + e*x)^(9/2)) + (256*b^4*(7*b*B*d
+ 10*A*b*e - 17*a*B*e)*(a + b*x)^(7/2))/(765765*e*(b*d - a*e)^6*(d + e*x)^(7/2))

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Rubi in Sympy [A]  time = 67.1479, size = 301, normalized size = 0.97 \[ \frac{256 b^{4} \left (a + b x\right )^{\frac{7}{2}} \left (10 A b e - 17 B a e + 7 B b d\right )}{765765 e \left (d + e x\right )^{\frac{7}{2}} \left (a e - b d\right )^{6}} - \frac{128 b^{3} \left (a + b x\right )^{\frac{7}{2}} \left (10 A b e - 17 B a e + 7 B b d\right )}{109395 e \left (d + e x\right )^{\frac{9}{2}} \left (a e - b d\right )^{5}} + \frac{32 b^{2} \left (a + b x\right )^{\frac{7}{2}} \left (10 A b e - 17 B a e + 7 B b d\right )}{12155 e \left (d + e x\right )^{\frac{11}{2}} \left (a e - b d\right )^{4}} - \frac{16 b \left (a + b x\right )^{\frac{7}{2}} \left (10 A b e - 17 B a e + 7 B b d\right )}{3315 e \left (d + e x\right )^{\frac{13}{2}} \left (a e - b d\right )^{3}} + \frac{2 \left (a + b x\right )^{\frac{7}{2}} \left (10 A b e - 17 B a e + 7 B b d\right )}{255 e \left (d + e x\right )^{\frac{15}{2}} \left (a e - b d\right )^{2}} - \frac{2 \left (a + b x\right )^{\frac{7}{2}} \left (A e - B d\right )}{17 e \left (d + e x\right )^{\frac{17}{2}} \left (a e - b d\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b*x+a)**(5/2)*(B*x+A)/(e*x+d)**(19/2),x)

[Out]

256*b**4*(a + b*x)**(7/2)*(10*A*b*e - 17*B*a*e + 7*B*b*d)/(765765*e*(d + e*x)**(
7/2)*(a*e - b*d)**6) - 128*b**3*(a + b*x)**(7/2)*(10*A*b*e - 17*B*a*e + 7*B*b*d)
/(109395*e*(d + e*x)**(9/2)*(a*e - b*d)**5) + 32*b**2*(a + b*x)**(7/2)*(10*A*b*e
- 17*B*a*e + 7*B*b*d)/(12155*e*(d + e*x)**(11/2)*(a*e - b*d)**4) - 16*b*(a + b*
x)**(7/2)*(10*A*b*e - 17*B*a*e + 7*B*b*d)/(3315*e*(d + e*x)**(13/2)*(a*e - b*d)*
*3) + 2*(a + b*x)**(7/2)*(10*A*b*e - 17*B*a*e + 7*B*b*d)/(255*e*(d + e*x)**(15/2
)*(a*e - b*d)**2) - 2*(a + b*x)**(7/2)*(A*e - B*d)/(17*e*(d + e*x)**(17/2)*(a*e
- b*d))

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Mathematica [A]  time = 0.877125, size = 331, normalized size = 1.07 \[ \frac{2 \sqrt{a+b x} \left (\frac{128 b^7 (d+e x)^8 (-17 a B e+10 A b e+7 b B d)}{(b d-a e)^6}+\frac{64 b^6 (d+e x)^7 (-17 a B e+10 A b e+7 b B d)}{(b d-a e)^5}+\frac{48 b^5 (d+e x)^6 (-17 a B e+10 A b e+7 b B d)}{(b d-a e)^4}+\frac{40 b^4 (d+e x)^5 (-17 a B e+10 A b e+7 b B d)}{(b d-a e)^3}+\frac{35 b^3 (d+e x)^4 (-17 a B e+10 A b e+7 b B d)}{(b d-a e)^2}-\frac{63 b^2 (d+e x)^3 (1207 a B e+5 A b e-1212 b B d)}{a e-b d}+231 b (d+e x)^2 (-527 a B e-275 A b e+802 b B d)-3003 (d+e x) (a e-b d) (17 a B e+35 A b e-52 b B d)+45045 (b d-a e)^2 (B d-A e)\right )}{765765 e^4 (d+e x)^{17/2}} \]

Antiderivative was successfully verified.

[In]  Integrate[((a + b*x)^(5/2)*(A + B*x))/(d + e*x)^(19/2),x]

[Out]

(2*Sqrt[a + b*x]*(45045*(b*d - a*e)^2*(B*d - A*e) - 3003*(-(b*d) + a*e)*(-52*b*B
*d + 35*A*b*e + 17*a*B*e)*(d + e*x) + 231*b*(802*b*B*d - 275*A*b*e - 527*a*B*e)*
(d + e*x)^2 - (63*b^2*(-1212*b*B*d + 5*A*b*e + 1207*a*B*e)*(d + e*x)^3)/(-(b*d)
+ a*e) + (35*b^3*(7*b*B*d + 10*A*b*e - 17*a*B*e)*(d + e*x)^4)/(b*d - a*e)^2 + (4
0*b^4*(7*b*B*d + 10*A*b*e - 17*a*B*e)*(d + e*x)^5)/(b*d - a*e)^3 + (48*b^5*(7*b*
B*d + 10*A*b*e - 17*a*B*e)*(d + e*x)^6)/(b*d - a*e)^4 + (64*b^6*(7*b*B*d + 10*A*
b*e - 17*a*B*e)*(d + e*x)^7)/(b*d - a*e)^5 + (128*b^7*(7*b*B*d + 10*A*b*e - 17*a
*B*e)*(d + e*x)^8)/(b*d - a*e)^6))/(765765*e^4*(d + e*x)^(17/2))

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Maple [B]  time = 0.017, size = 722, normalized size = 2.3 \[ -{\frac{-2560\,A{b}^{5}{e}^{5}{x}^{5}+4352\,Ba{b}^{4}{e}^{5}{x}^{5}-1792\,B{b}^{5}d{e}^{4}{x}^{5}+8960\,Aa{b}^{4}{e}^{5}{x}^{4}-21760\,A{b}^{5}d{e}^{4}{x}^{4}-15232\,B{a}^{2}{b}^{3}{e}^{5}{x}^{4}+43264\,Ba{b}^{4}d{e}^{4}{x}^{4}-15232\,B{b}^{5}{d}^{2}{e}^{3}{x}^{4}-20160\,A{a}^{2}{b}^{3}{e}^{5}{x}^{3}+76160\,Aa{b}^{4}d{e}^{4}{x}^{3}-81600\,A{b}^{5}{d}^{2}{e}^{3}{x}^{3}+34272\,B{a}^{3}{b}^{2}{e}^{5}{x}^{3}-143584\,B{a}^{2}{b}^{3}d{e}^{4}{x}^{3}+192032\,Ba{b}^{4}{d}^{2}{e}^{3}{x}^{3}-57120\,B{b}^{5}{d}^{3}{e}^{2}{x}^{3}+36960\,A{a}^{3}{b}^{2}{e}^{5}{x}^{2}-171360\,A{a}^{2}{b}^{3}d{e}^{4}{x}^{2}+285600\,Aa{b}^{4}{d}^{2}{e}^{3}{x}^{2}-176800\,A{b}^{5}{d}^{3}{e}^{2}{x}^{2}-62832\,B{a}^{4}b{e}^{5}{x}^{2}+317184\,B{a}^{3}{b}^{2}d{e}^{4}{x}^{2}-605472\,B{a}^{2}{b}^{3}{d}^{2}{e}^{3}{x}^{2}+500480\,Ba{b}^{4}{d}^{3}{e}^{2}{x}^{2}-123760\,B{b}^{5}{d}^{4}e{x}^{2}-60060\,A{a}^{4}b{e}^{5}x+314160\,A{a}^{3}{b}^{2}d{e}^{4}x-642600\,A{a}^{2}{b}^{3}{d}^{2}{e}^{3}x+618800\,Aa{b}^{4}{d}^{3}{e}^{2}x-243100\,A{b}^{5}{d}^{4}ex+102102\,B{a}^{5}{e}^{5}x-576114\,B{a}^{4}bd{e}^{4}x+1312332\,B{a}^{3}{b}^{2}{d}^{2}{e}^{3}x-1501780\,B{a}^{2}{b}^{3}{d}^{3}{e}^{2}x+846430\,Ba{b}^{4}{d}^{4}ex-170170\,B{b}^{5}{d}^{5}x+90090\,A{a}^{5}{e}^{5}-510510\,A{a}^{4}bd{e}^{4}+1178100\,A{a}^{3}{b}^{2}{d}^{2}{e}^{3}-1392300\,A{a}^{2}{b}^{3}{d}^{3}{e}^{2}+850850\,Aa{b}^{4}{d}^{4}e-218790\,A{b}^{5}{d}^{5}+12012\,B{a}^{5}d{e}^{4}-62832\,B{a}^{4}b{d}^{2}{e}^{3}+128520\,B{a}^{3}{b}^{2}{d}^{3}{e}^{2}-123760\,B{a}^{2}{b}^{3}{d}^{4}e+48620\,Ba{b}^{4}{d}^{5}}{765765\,{a}^{6}{e}^{6}-4594590\,{a}^{5}bd{e}^{5}[phone]\,{a}^{4}{b}^{2}{d}^{2}{e}^{4}-15315300\,{a}^{3}{b}^{3}{d}^{3}{e}^{3}[phone]\,{a}^{2}{b}^{4}{d}^{4}{e}^{2}-4594590\,a{b}^{5}{d}^{5}e+765765\,{b}^{6}{d}^{6}} \left ( bx+a \right ) ^{{\frac{7}{2}}} \left ( ex+d \right ) ^{-{\frac{17}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b*x+a)^(5/2)*(B*x+A)/(e*x+d)^(19/2),x)

[Out]

-2/765765*(b*x+a)^(7/2)*(-1280*A*b^5*e^5*x^5+2176*B*a*b^4*e^5*x^5-896*B*b^5*d*e^
4*x^5+4480*A*a*b^4*e^5*x^4-10880*A*b^5*d*e^4*x^4-7616*B*a^2*b^3*e^5*x^4+21632*B*
a*b^4*d*e^4*x^4-7616*B*b^5*d^2*e^3*x^4-10080*A*a^2*b^3*e^5*x^3+38080*A*a*b^4*d*e
^4*x^3-40800*A*b^5*d^2*e^3*x^3+17136*B*a^3*b^2*e^5*x^3-71792*B*a^2*b^3*d*e^4*x^3
+96016*B*a*b^4*d^2*e^3*x^3-28560*B*b^5*d^3*e^2*x^3+18480*A*a^3*b^2*e^5*x^2-85680
*A*a^2*b^3*d*e^4*x^2+142800*A*a*b^4*d^2*e^3*x^2-88400*A*b^5*d^3*e^2*x^2-31416*B*
a^4*b*e^5*x^2+158592*B*a^3*b^2*d*e^4*x^2-302736*B*a^2*b^3*d^2*e^3*x^2+250240*B*a
*b^4*d^3*e^2*x^2-61880*B*b^5*d^4*e*x^2-30030*A*a^4*b*e^5*x+157080*A*a^3*b^2*d*e^
4*x-321300*A*a^2*b^3*d^2*e^3*x+309400*A*a*b^4*d^3*e^2*x-121550*A*b^5*d^4*e*x+510
51*B*a^5*e^5*x-288057*B*a^4*b*d*e^4*x+656166*B*a^3*b^2*d^2*e^3*x-750890*B*a^2*b^
3*d^3*e^2*x+423215*B*a*b^4*d^4*e*x-85085*B*b^5*d^5*x+45045*A*a^5*e^5-255255*A*a^
4*b*d*e^4+589050*A*a^3*b^2*d^2*e^3-696150*A*a^2*b^3*d^3*e^2+425425*A*a*b^4*d^4*e
-109395*A*b^5*d^5+6006*B*a^5*d*e^4-31416*B*a^4*b*d^2*e^3+64260*B*a^3*b^2*d^3*e^2
-61880*B*a^2*b^3*d^4*e+24310*B*a*b^4*d^5)/(e*x+d)^(17/2)/(a^6*e^6-6*a^5*b*d*e^5+
15*a^4*b^2*d^2*e^4-20*a^3*b^3*d^3*e^3+15*a^2*b^4*d^4*e^2-6*a*b^5*d^5*e+b^6*d^6)

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Maxima [F]  time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((B*x + A)*(b*x + a)^(5/2)/(e*x + d)^(19/2),x, algorithm="maxima")

[Out]

Exception raised: ValueError

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Fricas [A]  time = 68.8735, size = 2603, normalized size = 8.42 \[ \text{result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((B*x + A)*(b*x + a)^(5/2)/(e*x + d)^(19/2),x, algorithm="fricas")

[Out]

-2/765765*(45045*A*a^8*e^5 - 128*(7*B*b^8*d*e^4 - (17*B*a*b^7 - 10*A*b^8)*e^5)*x
^8 - 64*(119*B*b^8*d^2*e^3 - 2*(148*B*a*b^7 - 85*A*b^8)*d*e^4 + (17*B*a^2*b^6 -
10*A*a*b^7)*e^5)*x^7 - 16*(1785*B*b^8*d^3*e^2 - 17*(269*B*a*b^7 - 150*A*b^8)*d^2
*e^3 + (599*B*a^2*b^6 - 340*A*a*b^7)*d*e^4 - 3*(17*B*a^3*b^5 - 10*A*a^2*b^6)*e^5
)*x^6 + 12155*(2*B*a^4*b^4 - 9*A*a^3*b^5)*d^5 - 7735*(8*B*a^5*b^3 - 55*A*a^4*b^4
)*d^4*e + 10710*(6*B*a^6*b^2 - 65*A*a^5*b^3)*d^3*e^2 - 7854*(4*B*a^7*b - 75*A*a^
6*b^2)*d^2*e^3 + 3003*(2*B*a^8 - 85*A*a^7*b)*d*e^4 - 8*(7735*B*b^8*d^4*e - 170*(
121*B*a*b^7 - 65*A*b^8)*d^3*e^2 + 102*(46*B*a^2*b^6 - 25*A*a*b^7)*d^2*e^3 - 2*(4
51*B*a^3*b^5 - 255*A*a^2*b^6)*d*e^4 + 5*(17*B*a^4*b^4 - 10*A*a^3*b^5)*e^5)*x^5 -
5*(17017*B*b^8*d^5 - 1105*(43*B*a*b^7 - 22*A*b^8)*d^4*e + 170*(101*B*a^2*b^6 -
52*A*a*b^7)*d^3*e^2 - 34*(167*B*a^3*b^5 - 90*A*a^2*b^6)*d^2*e^3 + 5*(241*B*a^4*b
^4 - 136*A*a^3*b^5)*d*e^4 - 7*(17*B*a^5*b^3 - 10*A*a^4*b^4)*e^5)*x^4 - (12155*(1
9*B*a*b^7 + 9*A*b^8)*d^5 - 5525*(185*B*a^2*b^6 + 11*A*a*b^7)*d^4*e + 2550*(575*B
*a^3*b^5 + 13*A*a^2*b^6)*d^3*e^2 - 170*(6617*B*a^4*b^4 + 75*A*a^3*b^5)*d^2*e^3 +
7*(64883*B*a^5*b^3 + 425*A*a^4*b^4)*d*e^4 - 63*(1207*B*a^6*b^2 + 5*A*a^5*b^3)*e
^5)*x^3 - (36465*(5*B*a^2*b^6 + 9*A*a*b^7)*d^5 - 27625*(37*B*a^3*b^5 + 33*A*a^2*
b^6)*d^4*e + 850*(2129*B*a^4*b^4 + 1469*A*a^3*b^5)*d^3*e^2 - 714*(2201*B*a^5*b^3
+ 1325*A*a^4*b^4)*d^2*e^3 + 21*(32741*B*a^6*b^2 + 18105*A*a^5*b^3)*d*e^4 - 231*
(527*B*a^7*b + 275*A*a^6*b^2)*e^5)*x^2 - (12155*(B*a^3*b^5 + 27*A*a^2*b^6)*d^5 -
5525*(43*B*a^4*b^4 + 209*A*a^3*b^5)*d^4*e + 1190*(469*B*a^5*b^3 + 1495*A*a^4*b^
4)*d^3*e^2 - 714*(787*B*a^6*b^2 + 2025*A*a^5*b^3)*d^2*e^3 + 231*(1169*B*a^7*b +
2635*A*a^6*b^2)*d*e^4 - 3003*(17*B*a^8 + 35*A*a^7*b)*e^5)*x)*sqrt(b*x + a)*sqrt(
e*x + d)/(b^6*d^15 - 6*a*b^5*d^14*e + 15*a^2*b^4*d^13*e^2 - 20*a^3*b^3*d^12*e^3
+ 15*a^4*b^2*d^11*e^4 - 6*a^5*b*d^10*e^5 + a^6*d^9*e^6 + (b^6*d^6*e^9 - 6*a*b^5*
d^5*e^10 + 15*a^2*b^4*d^4*e^11 - 20*a^3*b^3*d^3*e^12 + 15*a^4*b^2*d^2*e^13 - 6*a
^5*b*d*e^14 + a^6*e^15)*x^9 + 9*(b^6*d^7*e^8 - 6*a*b^5*d^6*e^9 + 15*a^2*b^4*d^5*
e^10 - 20*a^3*b^3*d^4*e^11 + 15*a^4*b^2*d^3*e^12 - 6*a^5*b*d^2*e^13 + a^6*d*e^14
)*x^8 + 36*(b^6*d^8*e^7 - 6*a*b^5*d^7*e^8 + 15*a^2*b^4*d^6*e^9 - 20*a^3*b^3*d^5*
e^10 + 15*a^4*b^2*d^4*e^11 - 6*a^5*b*d^3*e^12 + a^6*d^2*e^13)*x^7 + 84*(b^6*d^9*
e^6 - 6*a*b^5*d^8*e^7 + 15*a^2*b^4*d^7*e^8 - 20*a^3*b^3*d^6*e^9 + 15*a^4*b^2*d^5
*e^10 - 6*a^5*b*d^4*e^11 + a^6*d^3*e^12)*x^6 + 126*(b^6*d^10*e^5 - 6*a*b^5*d^9*e
^6 + 15*a^2*b^4*d^8*e^7 - 20*a^3*b^3*d^7*e^8 + 15*a^4*b^2*d^6*e^9 - 6*a^5*b*d^5*
e^10 + a^6*d^4*e^11)*x^5 + 126*(b^6*d^11*e^4 - 6*a*b^5*d^10*e^5 + 15*a^2*b^4*d^9
*e^6 - 20*a^3*b^3*d^8*e^7 + 15*a^4*b^2*d^7*e^8 - 6*a^5*b*d^6*e^9 + a^6*d^5*e^10)
*x^4 + 84*(b^6*d^12*e^3 - 6*a*b^5*d^11*e^4 + 15*a^2*b^4*d^10*e^5 - 20*a^3*b^3*d^
9*e^6 + 15*a^4*b^2*d^8*e^7 - 6*a^5*b*d^7*e^8 + a^6*d^6*e^9)*x^3 + 36*(b^6*d^13*e
^2 - 6*a*b^5*d^12*e^3 + 15*a^2*b^4*d^11*e^4 - 20*a^3*b^3*d^10*e^5 + 15*a^4*b^2*d
^9*e^6 - 6*a^5*b*d^8*e^7 + a^6*d^7*e^8)*x^2 + 9*(b^6*d^14*e - 6*a*b^5*d^13*e^2 +
15*a^2*b^4*d^12*e^3 - 20*a^3*b^3*d^11*e^4 + 15*a^4*b^2*d^10*e^5 - 6*a^5*b*d^9*e
^6 + a^6*d^8*e^7)*x)

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Sympy [F(-1)]  time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b*x+a)**(5/2)*(B*x+A)/(e*x+d)**(19/2),x)

[Out]

Timed out

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GIAC/XCAS [A]  time = 1.01832, size = 1, normalized size = 0. \[ \mathit{Done} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((B*x + A)*(b*x + a)^(5/2)/(e*x + d)^(19/2),x, algorithm="giac")

[Out]

Done