3.2010 \(\int \frac{(2+3 x) (3+5 x)^3}{\sqrt{1-2 x}} \, dx\)

Optimal. Leaf size=66 \[ -\frac{125}{48} (1-2 x)^{9/2}+\frac{1675}{56} (1-2 x)^{7/2}-\frac{561}{4} (1-2 x)^{5/2}+\frac{2783}{8} (1-2 x)^{3/2}-\frac{9317}{16} \sqrt{1-2 x} \]

[Out]

(-9317*Sqrt[1 - 2*x])/16 + (2783*(1 - 2*x)^(3/2))/8 - (561*(1 - 2*x)^(5/2))/4 +
(1675*(1 - 2*x)^(7/2))/56 - (125*(1 - 2*x)^(9/2))/48

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Rubi [A]  time = 0.0571125, antiderivative size = 66, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ -\frac{125}{48} (1-2 x)^{9/2}+\frac{1675}{56} (1-2 x)^{7/2}-\frac{561}{4} (1-2 x)^{5/2}+\frac{2783}{8} (1-2 x)^{3/2}-\frac{9317}{16} \sqrt{1-2 x} \]

Antiderivative was successfully verified.

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

[Out]

(-9317*Sqrt[1 - 2*x])/16 + (2783*(1 - 2*x)^(3/2))/8 - (561*(1 - 2*x)^(5/2))/4 +
(1675*(1 - 2*x)^(7/2))/56 - (125*(1 - 2*x)^(9/2))/48

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Rubi in Sympy [A]  time = 8.3832, size = 58, normalized size = 0.88 \[ - \frac{125 \left (- 2 x + 1\right )^{\frac{9}{2}}}{48} + \frac{1675 \left (- 2 x + 1\right )^{\frac{7}{2}}}{56} - \frac{561 \left (- 2 x + 1\right )^{\frac{5}{2}}}{4} + \frac{2783 \left (- 2 x + 1\right )^{\frac{3}{2}}}{8} - \frac{9317 \sqrt{- 2 x + 1}}{16} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-125*(-2*x + 1)**(9/2)/48 + 1675*(-2*x + 1)**(7/2)/56 - 561*(-2*x + 1)**(5/2)/4
+ 2783*(-2*x + 1)**(3/2)/8 - 9317*sqrt(-2*x + 1)/16

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Mathematica [A]  time = 0.0327957, size = 33, normalized size = 0.5 \[ -\frac{1}{21} \sqrt{1-2 x} \left (875 x^4+3275 x^3+5556 x^2+6161 x+7295\right ) \]

Antiderivative was successfully verified.

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

[Out]

-(Sqrt[1 - 2*x]*(7295 + 6161*x + 5556*x^2 + 3275*x^3 + 875*x^4))/21

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Maple [A]  time = 0.004, size = 30, normalized size = 0.5 \[ -{\frac{875\,{x}^{4}+3275\,{x}^{3}+5556\,{x}^{2}+6161\,x+7295}{21}\sqrt{1-2\,x}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/21*(875*x^4+3275*x^3+5556*x^2+6161*x+7295)*(1-2*x)^(1/2)

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Maxima [A]  time = 1.37051, size = 62, normalized size = 0.94 \[ -\frac{125}{48} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} + \frac{1675}{56} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} - \frac{561}{4} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{2783}{8} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{9317}{16} \, \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-125/48*(-2*x + 1)^(9/2) + 1675/56*(-2*x + 1)^(7/2) - 561/4*(-2*x + 1)^(5/2) + 2
783/8*(-2*x + 1)^(3/2) - 9317/16*sqrt(-2*x + 1)

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Fricas [A]  time = 0.232528, size = 39, normalized size = 0.59 \[ -\frac{1}{21} \,{\left (875 \, x^{4} + 3275 \, x^{3} + 5556 \, x^{2} + 6161 \, x + 7295\right )} \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/21*(875*x^4 + 3275*x^3 + 5556*x^2 + 6161*x + 7295)*sqrt(-2*x + 1)

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Sympy [A]  time = 9.88824, size = 58, normalized size = 0.88 \[ - \frac{125 \left (- 2 x + 1\right )^{\frac{9}{2}}}{48} + \frac{1675 \left (- 2 x + 1\right )^{\frac{7}{2}}}{56} - \frac{561 \left (- 2 x + 1\right )^{\frac{5}{2}}}{4} + \frac{2783 \left (- 2 x + 1\right )^{\frac{3}{2}}}{8} - \frac{9317 \sqrt{- 2 x + 1}}{16} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-125*(-2*x + 1)**(9/2)/48 + 1675*(-2*x + 1)**(7/2)/56 - 561*(-2*x + 1)**(5/2)/4
+ 2783*(-2*x + 1)**(3/2)/8 - 9317*sqrt(-2*x + 1)/16

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GIAC/XCAS [A]  time = 0.241808, size = 90, normalized size = 1.36 \[ -\frac{125}{48} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} - \frac{1675}{56} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} - \frac{561}{4} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{2783}{8} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{9317}{16} \, \sqrt{-2 \, x + 1} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-125/48*(2*x - 1)^4*sqrt(-2*x + 1) - 1675/56*(2*x - 1)^3*sqrt(-2*x + 1) - 561/4*
(2*x - 1)^2*sqrt(-2*x + 1) + 2783/8*(-2*x + 1)^(3/2) - 9317/16*sqrt(-2*x + 1)