3.1801 \(\int \sqrt{1-2 x} (2+3 x) (3+5 x)^3 \, dx\)

Optimal. Leaf size=66 \[ -\frac{375}{176} (1-2 x)^{11/2}+\frac{1675}{72} (1-2 x)^{9/2}-\frac{2805}{28} (1-2 x)^{7/2}+\frac{8349}{40} (1-2 x)^{5/2}-\frac{9317}{48} (1-2 x)^{3/2} \]

[Out]

(-9317*(1 - 2*x)^(3/2))/48 + (8349*(1 - 2*x)^(5/2))/40 - (2805*(1 - 2*x)^(7/2))/
28 + (1675*(1 - 2*x)^(9/2))/72 - (375*(1 - 2*x)^(11/2))/176

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Rubi [A]  time = 0.0501929, 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 \[ -\frac{375}{176} (1-2 x)^{11/2}+\frac{1675}{72} (1-2 x)^{9/2}-\frac{2805}{28} (1-2 x)^{7/2}+\frac{8349}{40} (1-2 x)^{5/2}-\frac{9317}{48} (1-2 x)^{3/2} \]

Antiderivative was successfully verified.

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

[Out]

(-9317*(1 - 2*x)^(3/2))/48 + (8349*(1 - 2*x)^(5/2))/40 - (2805*(1 - 2*x)^(7/2))/
28 + (1675*(1 - 2*x)^(9/2))/72 - (375*(1 - 2*x)^(11/2))/176

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Rubi in Sympy [A]  time = 7.77331, size = 58, normalized size = 0.88 \[ - \frac{375 \left (- 2 x + 1\right )^{\frac{11}{2}}}{176} + \frac{1675 \left (- 2 x + 1\right )^{\frac{9}{2}}}{72} - \frac{2805 \left (- 2 x + 1\right )^{\frac{7}{2}}}{28} + \frac{8349 \left (- 2 x + 1\right )^{\frac{5}{2}}}{40} - \frac{9317 \left (- 2 x + 1\right )^{\frac{3}{2}}}{48} \]

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]

-375*(-2*x + 1)**(11/2)/176 + 1675*(-2*x + 1)**(9/2)/72 - 2805*(-2*x + 1)**(7/2)
/28 + 8349*(-2*x + 1)**(5/2)/40 - 9317*(-2*x + 1)**(3/2)/48

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Mathematica [A]  time = 0.0282996, size = 38, normalized size = 0.58 \[ \frac{\sqrt{1-2 x} \left (236250 x^5+699125 x^4+788075 x^3+366816 x^2-36121 x-223231\right )}{3465} \]

Antiderivative was successfully verified.

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

[Out]

(Sqrt[1 - 2*x]*(-223231 - 36121*x + 366816*x^2 + 788075*x^3 + 699125*x^4 + 23625
0*x^5))/3465

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Maple [A]  time = 0.005, size = 30, normalized size = 0.5 \[ -{\frac{118125\,{x}^{4}+408625\,{x}^{3}+598350\,{x}^{2}+482583\,x+223231}{3465} \left ( 1-2\,x \right ) ^{{\frac{3}{2}}}} \]

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]

-1/3465*(118125*x^4+408625*x^3+598350*x^2+482583*x+223231)*(1-2*x)^(3/2)

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Maxima [A]  time = 1.39515, size = 62, normalized size = 0.94 \[ -\frac{375}{176} \,{\left (-2 \, x + 1\right )}^{\frac{11}{2}} + \frac{1675}{72} \,{\left (-2 \, x + 1\right )}^{\frac{9}{2}} - \frac{2805}{28} \,{\left (-2 \, x + 1\right )}^{\frac{7}{2}} + \frac{8349}{40} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - \frac{9317}{48} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} \]

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]

-375/176*(-2*x + 1)^(11/2) + 1675/72*(-2*x + 1)^(9/2) - 2805/28*(-2*x + 1)^(7/2)
+ 8349/40*(-2*x + 1)^(5/2) - 9317/48*(-2*x + 1)^(3/2)

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Fricas [A]  time = 0.208789, size = 46, normalized size = 0.7 \[ \frac{1}{3465} \,{\left (236250 \, x^{5} + 699125 \, x^{4} + 788075 \, x^{3} + 366816 \, x^{2} - 36121 \, x - 223231\right )} \sqrt{-2 \, x + 1} \]

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]

1/3465*(236250*x^5 + 699125*x^4 + 788075*x^3 + 366816*x^2 - 36121*x - 223231)*sq
rt(-2*x + 1)

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Sympy [A]  time = 3.02685, size = 58, normalized size = 0.88 \[ - \frac{375 \left (- 2 x + 1\right )^{\frac{11}{2}}}{176} + \frac{1675 \left (- 2 x + 1\right )^{\frac{9}{2}}}{72} - \frac{2805 \left (- 2 x + 1\right )^{\frac{7}{2}}}{28} + \frac{8349 \left (- 2 x + 1\right )^{\frac{5}{2}}}{40} - \frac{9317 \left (- 2 x + 1\right )^{\frac{3}{2}}}{48} \]

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]

-375*(-2*x + 1)**(11/2)/176 + 1675*(-2*x + 1)**(9/2)/72 - 2805*(-2*x + 1)**(7/2)
/28 + 8349*(-2*x + 1)**(5/2)/40 - 9317*(-2*x + 1)**(3/2)/48

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GIAC/XCAS [A]  time = 0.233131, size = 100, normalized size = 1.52 \[ \frac{375}{176} \,{\left (2 \, x - 1\right )}^{5} \sqrt{-2 \, x + 1} + \frac{1675}{72} \,{\left (2 \, x - 1\right )}^{4} \sqrt{-2 \, x + 1} + \frac{2805}{28} \,{\left (2 \, x - 1\right )}^{3} \sqrt{-2 \, x + 1} + \frac{8349}{40} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} - \frac{9317}{48} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} \]

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]

375/176*(2*x - 1)^5*sqrt(-2*x + 1) + 1675/72*(2*x - 1)^4*sqrt(-2*x + 1) + 2805/2
8*(2*x - 1)^3*sqrt(-2*x + 1) + 8349/40*(2*x - 1)^2*sqrt(-2*x + 1) - 9317/48*(-2*
x + 1)^(3/2)