3.2067 \(\int \frac{(2+3 x)^4 (3+5 x)^2}{(1-2 x)^{3/2}} \, dx\)

Optimal. Leaf size=92 \[ -\frac{2025}{704} (1-2 x)^{11/2}+\frac{1545}{32} (1-2 x)^{9/2}-\frac{159111}{448} (1-2 x)^{7/2}+\frac{121359}{80} (1-2 x)^{5/2}-\frac{832951}{192} (1-2 x)^{3/2}+\frac{381073}{32} \sqrt{1-2 x}+\frac{290521}{64 \sqrt{1-2 x}} \]

[Out]

290521/(64*Sqrt[1 - 2*x]) + (381073*Sqrt[1 - 2*x])/32 - (832951*(1 - 2*x)^(3/2))
/192 + (121359*(1 - 2*x)^(5/2))/80 - (159111*(1 - 2*x)^(7/2))/448 + (1545*(1 - 2
*x)^(9/2))/32 - (2025*(1 - 2*x)^(11/2))/704

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Rubi [A]  time = 0.0782221, antiderivative size = 92, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.042 \[ -\frac{2025}{704} (1-2 x)^{11/2}+\frac{1545}{32} (1-2 x)^{9/2}-\frac{159111}{448} (1-2 x)^{7/2}+\frac{121359}{80} (1-2 x)^{5/2}-\frac{832951}{192} (1-2 x)^{3/2}+\frac{381073}{32} \sqrt{1-2 x}+\frac{290521}{64 \sqrt{1-2 x}} \]

Antiderivative was successfully verified.

[In]  Int[((2 + 3*x)^4*(3 + 5*x)^2)/(1 - 2*x)^(3/2),x]

[Out]

290521/(64*Sqrt[1 - 2*x]) + (381073*Sqrt[1 - 2*x])/32 - (832951*(1 - 2*x)^(3/2))
/192 + (121359*(1 - 2*x)^(5/2))/80 - (159111*(1 - 2*x)^(7/2))/448 + (1545*(1 - 2
*x)^(9/2))/32 - (2025*(1 - 2*x)^(11/2))/704

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Rubi in Sympy [A]  time = 10.7827, size = 82, normalized size = 0.89 \[ - \frac{2025 \left (- 2 x + 1\right )^{\frac{11}{2}}}{704} + \frac{1545 \left (- 2 x + 1\right )^{\frac{9}{2}}}{32} - \frac{159111 \left (- 2 x + 1\right )^{\frac{7}{2}}}{448} + \frac{121359 \left (- 2 x + 1\right )^{\frac{5}{2}}}{80} - \frac{832951 \left (- 2 x + 1\right )^{\frac{3}{2}}}{192} + \frac{381073 \sqrt{- 2 x + 1}}{32} + \frac{290521}{64 \sqrt{- 2 x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((2+3*x)**4*(3+5*x)**2/(1-2*x)**(3/2),x)

[Out]

-2025*(-2*x + 1)**(11/2)/704 + 1545*(-2*x + 1)**(9/2)/32 - 159111*(-2*x + 1)**(7
/2)/448 + 121359*(-2*x + 1)**(5/2)/80 - 832951*(-2*x + 1)**(3/2)/192 + 381073*sq
rt(-2*x + 1)/32 + 290521/(64*sqrt(-2*x + 1))

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Mathematica [A]  time = 0.0562684, size = 43, normalized size = 0.47 \[ \frac{-212625 x^6-1146600 x^5-2899485 x^4-4819932 x^3-6831172 x^2-15214664 x+15380984}{1155 \sqrt{1-2 x}} \]

Antiderivative was successfully verified.

[In]  Integrate[((2 + 3*x)^4*(3 + 5*x)^2)/(1 - 2*x)^(3/2),x]

[Out]

(15380984 - 15214664*x - 6831172*x^2 - 4819932*x^3 - 2899485*x^4 - 1146600*x^5 -
212625*x^6)/(1155*Sqrt[1 - 2*x])

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Maple [A]  time = 0.006, size = 40, normalized size = 0.4 \[ -{\frac{212625\,{x}^{6}+1146600\,{x}^{5}+2899485\,{x}^{4}+4819932\,{x}^{3}+6831172\,{x}^{2}[phone]\,x-15380984}{1155}{\frac{1}{\sqrt{1-2\,x}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((2+3*x)^4*(3+5*x)^2/(1-2*x)^(3/2),x)

[Out]

-1/1155*(212625*x^6+1146600*x^5+2899485*x^4+4819932*x^3+6831172*x^2+15214664*x-1
5380984)/(1-2*x)^(1/2)

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Maxima [A]  time = 1.34377, size = 86, normalized size = 0.93 \[ -\frac{2025}{704} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{1545}{32} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{159111}{448} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} + \frac{121359}{80} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - \frac{832951}{192} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{381073}{32} \, \sqrt{-2 \, x + 1} + \frac{290521}{64 \, \sqrt{-2 \, x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^2*(3*x + 2)^4/(-2*x + 1)^(3/2),x, algorithm="maxima")

[Out]

-2025/704*(-2*x + 1)^(11/2) + 1545/32*(-2*x + 1)^(9/2) - 159111/448*(-2*x + 1)^(
7/2) + 121359/80*(-2*x + 1)^(5/2) - 832951/192*(-2*x + 1)^(3/2) + 381073/32*sqrt
(-2*x + 1) + 290521/64/sqrt(-2*x + 1)

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Fricas [A]  time = 0.22042, size = 53, normalized size = 0.58 \[ -\frac{212625 \, x^{6} + 1146600 \, x^{5} + 2899485 \, x^{4} + 4819932 \, x^{3} + 6831172 \, x^{2} + 15214664 \, x - 15380984}{1155 \, \sqrt{-2 \, x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^2*(3*x + 2)^4/(-2*x + 1)^(3/2),x, algorithm="fricas")

[Out]

-1/1155*(212625*x^6 + 1146600*x^5 + 2899485*x^4 + 4819932*x^3 + 6831172*x^2 + 15
214664*x - 15380984)/sqrt(-2*x + 1)

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Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (3 x + 2\right )^{4} \left (5 x + 3\right )^{2}}{\left (- 2 x + 1\right )^{\frac{3}{2}}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((2+3*x)**4*(3+5*x)**2/(1-2*x)**(3/2),x)

[Out]

Integral((3*x + 2)**4*(5*x + 3)**2/(-2*x + 1)**(3/2), x)

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GIAC/XCAS [A]  time = 0.210351, size = 124, normalized size = 1.35 \[ \frac{2025}{704} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} + \frac{1545}{32} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{159111}{448} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + \frac{121359}{80} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - \frac{832951}{192} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{381073}{32} \, \sqrt{-2 \, x + 1} + \frac{290521}{64 \, \sqrt{-2 \, x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((5*x + 3)^2*(3*x + 2)^4/(-2*x + 1)^(3/2),x, algorithm="giac")

[Out]

2025/704*(2*x - 1)^5*sqrt(-2*x + 1) + 1545/32*(2*x - 1)^4*sqrt(-2*x + 1) + 15911
1/448*(2*x - 1)^3*sqrt(-2*x + 1) + 121359/80*(2*x - 1)^2*sqrt(-2*x + 1) - 832951
/192*(-2*x + 1)^(3/2) + 381073/32*sqrt(-2*x + 1) + 290521/64/sqrt(-2*x + 1)