Optimal. Leaf size=66 \[ -\frac{75}{16} (1-2 x)^{5/2}+\frac{1675}{24} (1-2 x)^{3/2}-\frac{2805}{4} \sqrt{1-2 x}-\frac{8349}{8 \sqrt{1-2 x}}+\frac{9317}{48 (1-2 x)^{3/2}} \]
[Out]
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Rubi [A] time = 0.0593476, 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 \[ -\frac{75}{16} (1-2 x)^{5/2}+\frac{1675}{24} (1-2 x)^{3/2}-\frac{2805}{4} \sqrt{1-2 x}-\frac{8349}{8 \sqrt{1-2 x}}+\frac{9317}{48 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
[In] Int[((2 + 3*x)*(3 + 5*x)^3)/(1 - 2*x)^(5/2),x]
[Out]
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Rubi in Sympy [A] time = 8.08477, size = 58, normalized size = 0.88 \[ - \frac{75 \left (- 2 x + 1\right )^{\frac{5}{2}}}{16} + \frac{1675 \left (- 2 x + 1\right )^{\frac{3}{2}}}{24} - \frac{2805 \sqrt{- 2 x + 1}}{4} - \frac{8349}{8 \sqrt{- 2 x + 1}} + \frac{9317}{48 \left (- 2 x + 1\right )^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)*(3+5*x)**3/(1-2*x)**(5/2),x)
[Out]
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Mathematica [A] time = 0.0448725, size = 33, normalized size = 0.5 \[ -\frac{225 x^4+1225 x^3+6240 x^2-13533 x+4457}{3 (1-2 x)^{3/2}} \]
Antiderivative was successfully verified.
[In] Integrate[((2 + 3*x)*(3 + 5*x)^3)/(1 - 2*x)^(5/2),x]
[Out]
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Maple [A] time = 0.005, size = 30, normalized size = 0.5 \[ -{\frac{225\,{x}^{4}+1225\,{x}^{3}+6240\,{x}^{2}-13533\,x+4457}{3} \left ( 1-2\,x \right ) ^{-{\frac{3}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)*(3+5*x)^3/(1-2*x)^(5/2),x)
[Out]
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Maxima [A] time = 1.36182, size = 57, normalized size = 0.86 \[ -\frac{75}{16} \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} + \frac{1675}{24} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{2805}{4} \, \sqrt{-2 \, x + 1} + \frac{121 \,{\left (828 \, x - 337\right )}}{48 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)/(-2*x + 1)^(5/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.212817, size = 49, normalized size = 0.74 \[ \frac{225 \, x^{4} + 1225 \, x^{3} + 6240 \, x^{2} - 13533 \, x + 4457}{3 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)/(-2*x + 1)^(5/2),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (3 x + 2\right ) \left (5 x + 3\right )^{3}}{\left (- 2 x + 1\right )^{\frac{5}{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)*(3+5*x)**3/(1-2*x)**(5/2),x)
[Out]
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GIAC/XCAS [A] time = 0.214628, size = 76, normalized size = 1.15 \[ -\frac{75}{16} \,{\left (2 \, x - 1\right )}^{2} \sqrt{-2 \, x + 1} + \frac{1675}{24} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} - \frac{2805}{4} \, \sqrt{-2 \, x + 1} - \frac{121 \,{\left (828 \, x - 337\right )}}{48 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 3)^3*(3*x + 2)/(-2*x + 1)^(5/2),x, algorithm="giac")
[Out]