3.2066 \(\int \frac{(2+3 x)^5 (3+5 x)^2}{(1-2 x)^{3/2}} \, dx\)

Optimal. Leaf size=105 \[ \frac{6075 (1-2 x)^{13/2}}{1664}-\frac{97605 (1-2 x)^{11/2}}{1408}+\frac{74667}{128} (1-2 x)^{9/2}-\frac{367155}{128} (1-2 x)^{7/2}+\frac{1179381}{128} (1-2 x)^{5/2}-\frac{8117095}{384} (1-2 x)^{3/2}+\frac{6206585}{128} \sqrt{1-2 x}+\frac{2033647}{128 \sqrt{1-2 x}} \]

[Out]

2033647/(128*Sqrt[1 - 2*x]) + (6206585*Sqrt[1 - 2*x])/128 - (8117095*(1 - 2*x)^(
3/2))/384 + (1179381*(1 - 2*x)^(5/2))/128 - (367155*(1 - 2*x)^(7/2))/128 + (7466
7*(1 - 2*x)^(9/2))/128 - (97605*(1 - 2*x)^(11/2))/1408 + (6075*(1 - 2*x)^(13/2))
/1664

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Rubi [A]  time = 0.082826, antiderivative size = 105, 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 \[ \frac{6075 (1-2 x)^{13/2}}{1664}-\frac{97605 (1-2 x)^{11/2}}{1408}+\frac{74667}{128} (1-2 x)^{9/2}-\frac{367155}{128} (1-2 x)^{7/2}+\frac{1179381}{128} (1-2 x)^{5/2}-\frac{8117095}{384} (1-2 x)^{3/2}+\frac{6206585}{128} \sqrt{1-2 x}+\frac{2033647}{128 \sqrt{1-2 x}} \]

Antiderivative was successfully verified.

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

[Out]

2033647/(128*Sqrt[1 - 2*x]) + (6206585*Sqrt[1 - 2*x])/128 - (8117095*(1 - 2*x)^(
3/2))/384 + (1179381*(1 - 2*x)^(5/2))/128 - (367155*(1 - 2*x)^(7/2))/128 + (7466
7*(1 - 2*x)^(9/2))/128 - (97605*(1 - 2*x)^(11/2))/1408 + (6075*(1 - 2*x)^(13/2))
/1664

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Rubi in Sympy [A]  time = 12.1802, size = 94, normalized size = 0.9 \[ \frac{6075 \left (- 2 x + 1\right )^{\frac{13}{2}}}{1664} - \frac{97605 \left (- 2 x + 1\right )^{\frac{11}{2}}}{1408} + \frac{74667 \left (- 2 x + 1\right )^{\frac{9}{2}}}{128} - \frac{367155 \left (- 2 x + 1\right )^{\frac{7}{2}}}{128} + \frac{1179381 \left (- 2 x + 1\right )^{\frac{5}{2}}}{128} - \frac{8117095 \left (- 2 x + 1\right )^{\frac{3}{2}}}{384} + \frac{6206585 \sqrt{- 2 x + 1}}{128} + \frac{2033647}{128 \sqrt{- 2 x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

6075*(-2*x + 1)**(13/2)/1664 - 97605*(-2*x + 1)**(11/2)/1408 + 74667*(-2*x + 1)*
*(9/2)/128 - 367155*(-2*x + 1)**(7/2)/128 + 1179381*(-2*x + 1)**(5/2)/128 - 8117
095*(-2*x + 1)**(3/2)/384 + 6206585*sqrt(-2*x + 1)/128 + 2033647/(128*sqrt(-2*x
+ 1))

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Mathematica [A]  time = 0.062804, size = 48, normalized size = 0.46 \[ \frac{-200475 x^7-1201635 x^6-3350637 x^5-5928885 x^4-7945164 x^3-10015804 x^2-21370088 x+21493640}{429 \sqrt{1-2 x}} \]

Antiderivative was successfully verified.

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

[Out]

(21493640 - 21370088*x - 10015804*x^2 - 7945164*x^3 - 5928885*x^4 - 3350637*x^5
- 1201635*x^6 - 200475*x^7)/(429*Sqrt[1 - 2*x])

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Maple [A]  time = 0.007, size = 45, normalized size = 0.4 \[ -{\frac{200475\,{x}^{7}+1201635\,{x}^{6}+3350637\,{x}^{5}+5928885\,{x}^{4}+7945164\,{x}^{3}[phone]\,{x}^{2}[phone]\,x-21493640}{429}{\frac{1}{\sqrt{1-2\,x}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/429*(200475*x^7+1201635*x^6+3350637*x^5+5928885*x^4+7945164*x^3+10015804*x^2+
21370088*x-21493640)/(1-2*x)^(1/2)

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Maxima [A]  time = 1.34644, size = 99, normalized size = 0.94 \[ \frac{6075}{1664} \,{\left (-2 \, x + 1\right )}^{\frac{13}{2}} - \frac{97605}{1408} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{74667}{128} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{367155}{128} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} + \frac{1179381}{128} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - \frac{8117095}{384} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{6206585}{128} \, \sqrt{-2 \, x + 1} + \frac{2033647}{128 \, \sqrt{-2 \, x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

6075/1664*(-2*x + 1)^(13/2) - 97605/1408*(-2*x + 1)^(11/2) + 74667/128*(-2*x + 1
)^(9/2) - 367155/128*(-2*x + 1)^(7/2) + 1179381/128*(-2*x + 1)^(5/2) - 8117095/3
84*(-2*x + 1)^(3/2) + 6206585/128*sqrt(-2*x + 1) + 2033647/128/sqrt(-2*x + 1)

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Fricas [A]  time = 0.220073, size = 59, normalized size = 0.56 \[ -\frac{200475 \, x^{7} + 1201635 \, x^{6} + 3350637 \, x^{5} + 5928885 \, x^{4} + 7945164 \, x^{3} + 10015804 \, x^{2} + 21370088 \, x - 21493640}{429 \, \sqrt{-2 \, x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/429*(200475*x^7 + 1201635*x^6 + 3350637*x^5 + 5928885*x^4 + 7945164*x^3 + 100
15804*x^2 + 21370088*x - 21493640)/sqrt(-2*x + 1)

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

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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GIAC/XCAS [A]  time = 0.210878, size = 146, normalized size = 1.39 \[ \frac{6075}{1664} \,{\left (2 \, x - 1\right )}^{6} \sqrt{-2 \, x + 1} + \frac{97605}{1408} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} + \frac{74667}{128} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{367155}{128} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + \frac{1179381}{128} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - \frac{8117095}{384} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{6206585}{128} \, \sqrt{-2 \, x + 1} + \frac{2033647}{128 \, \sqrt{-2 \, x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

6075/1664*(2*x - 1)^6*sqrt(-2*x + 1) + 97605/1408*(2*x - 1)^5*sqrt(-2*x + 1) + 7
4667/128*(2*x - 1)^4*sqrt(-2*x + 1) + 367155/128*(2*x - 1)^3*sqrt(-2*x + 1) + 11
79381/128*(2*x - 1)^2*sqrt(-2*x + 1) - 8117095/384*(-2*x + 1)^(3/2) + 6206585/12
8*sqrt(-2*x + 1) + 2033647/128/sqrt(-2*x + 1)