3.2130 \(\int \frac{(2+3 x)^4 (3+5 x)^2}{(1-2 x)^{5/2}} \, dx\)

Optimal. Leaf size=92 \[ -\frac{225}{64} (1-2 x)^{9/2}+\frac{13905}{224} (1-2 x)^{7/2}-\frac{159111}{320} (1-2 x)^{5/2}+\frac{40453}{16} (1-2 x)^{3/2}-\frac{832951}{64} \sqrt{1-2 x}-\frac{381073}{32 \sqrt{1-2 x}}+\frac{290521}{192 (1-2 x)^{3/2}} \]

[Out]

290521/(192*(1 - 2*x)^(3/2)) - 381073/(32*Sqrt[1 - 2*x]) - (832951*Sqrt[1 - 2*x]
)/64 + (40453*(1 - 2*x)^(3/2))/16 - (159111*(1 - 2*x)^(5/2))/320 + (13905*(1 - 2
*x)^(7/2))/224 - (225*(1 - 2*x)^(9/2))/64

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Rubi [A]  time = 0.0808667, 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 \[ -\frac{225}{64} (1-2 x)^{9/2}+\frac{13905}{224} (1-2 x)^{7/2}-\frac{159111}{320} (1-2 x)^{5/2}+\frac{40453}{16} (1-2 x)^{3/2}-\frac{832951}{64} \sqrt{1-2 x}-\frac{381073}{32 \sqrt{1-2 x}}+\frac{290521}{192 (1-2 x)^{3/2}} \]

Antiderivative was successfully verified.

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

[Out]

290521/(192*(1 - 2*x)^(3/2)) - 381073/(32*Sqrt[1 - 2*x]) - (832951*Sqrt[1 - 2*x]
)/64 + (40453*(1 - 2*x)^(3/2))/16 - (159111*(1 - 2*x)^(5/2))/320 + (13905*(1 - 2
*x)^(7/2))/224 - (225*(1 - 2*x)^(9/2))/64

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Rubi in Sympy [A]  time = 10.613, size = 82, normalized size = 0.89 \[ - \frac{225 \left (- 2 x + 1\right )^{\frac{9}{2}}}{64} + \frac{13905 \left (- 2 x + 1\right )^{\frac{7}{2}}}{224} - \frac{159111 \left (- 2 x + 1\right )^{\frac{5}{2}}}{320} + \frac{40453 \left (- 2 x + 1\right )^{\frac{3}{2}}}{16} - \frac{832951 \sqrt{- 2 x + 1}}{64} - \frac{381073}{32 \sqrt{- 2 x + 1}} + \frac{290521}{192 \left (- 2 x + 1\right )^{\frac{3}{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-225*(-2*x + 1)**(9/2)/64 + 13905*(-2*x + 1)**(7/2)/224 - 159111*(-2*x + 1)**(5/
2)/320 + 40453*(-2*x + 1)**(3/2)/16 - 832951*sqrt(-2*x + 1)/64 - 381073/(32*sqrt
(-2*x + 1)) + 290521/(192*(-2*x + 1)**(3/2))

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Mathematica [A]  time = 0.0563055, size = 43, normalized size = 0.47 \[ -\frac{23625 x^6+137700 x^5+402489 x^4+915492 x^3+3294996 x^2-6731112 x+2238664}{105 (1-2 x)^{3/2}} \]

Antiderivative was successfully verified.

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

[Out]

-(2238664 - 6731112*x + 3294996*x^2 + 915492*x^3 + 402489*x^4 + 137700*x^5 + 236
25*x^6)/(105*(1 - 2*x)^(3/2))

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Maple [A]  time = 0.006, size = 40, normalized size = 0.4 \[ -{\frac{23625\,{x}^{6}+137700\,{x}^{5}+402489\,{x}^{4}+915492\,{x}^{3}+3294996\,{x}^{2}-6731112\,x+2238664}{105} \left ( 1-2\,x \right ) ^{-{\frac{3}{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/105*(23625*x^6+137700*x^5+402489*x^4+915492*x^3+3294996*x^2-6731112*x+2238664
)/(1-2*x)^(3/2)

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Maxima [A]  time = 1.35192, size = 81, normalized size = 0.88 \[ -\frac{225}{64} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{13905}{224} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{159111}{320} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{40453}{16} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{832951}{64} \, \sqrt{-2 \, x + 1} + \frac{3773 \,{\left (1212 \, x - 529\right )}}{192 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-225/64*(-2*x + 1)^(9/2) + 13905/224*(-2*x + 1)^(7/2) - 159111/320*(-2*x + 1)^(5
/2) + 40453/16*(-2*x + 1)^(3/2) - 832951/64*sqrt(-2*x + 1) + 3773/192*(1212*x -
529)/(-2*x + 1)^(3/2)

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Fricas [A]  time = 0.219461, size = 62, normalized size = 0.67 \[ \frac{23625 \, x^{6} + 137700 \, x^{5} + 402489 \, x^{4} + 915492 \, x^{3} + 3294996 \, x^{2} - 6731112 \, x + 2238664}{105 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

1/105*(23625*x^6 + 137700*x^5 + 402489*x^4 + 915492*x^3 + 3294996*x^2 - 6731112*
x + 2238664)/((2*x - 1)*sqrt(-2*x + 1))

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

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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GIAC/XCAS [A]  time = 0.211987, size = 119, normalized size = 1.29 \[ -\frac{225}{64} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - \frac{13905}{224} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{159111}{320} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{40453}{16} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{832951}{64} \, \sqrt{-2 \, x + 1} - \frac{3773 \,{\left (1212 \, x - 529\right )}}{192 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-225/64*(2*x - 1)^4*sqrt(-2*x + 1) - 13905/224*(2*x - 1)^3*sqrt(-2*x + 1) - 1591
11/320*(2*x - 1)^2*sqrt(-2*x + 1) + 40453/16*(-2*x + 1)^(3/2) - 832951/64*sqrt(-
2*x + 1) - 3773/192*(1212*x - 529)/((2*x - 1)*sqrt(-2*x + 1))