Optimal. Leaf size=120 \[ \frac{7 (3 x+2)^4}{33 (1-2 x)^{3/2} (5 x+3)}-\frac{38 (3 x+2)^3}{1815 \sqrt{1-2 x} (5 x+3)}-\frac{7588 (3 x+2)^2}{6655 \sqrt{1-2 x}}-\frac{6 \sqrt{1-2 x} (38025 x+114092)}{33275}-\frac{68 \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )}{33275 \sqrt{55}} \]
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Rubi [A] time = 0.239789, antiderivative size = 120, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 6, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25 \[ \frac{7 (3 x+2)^4}{33 (1-2 x)^{3/2} (5 x+3)}-\frac{38 (3 x+2)^3}{1815 \sqrt{1-2 x} (5 x+3)}-\frac{7588 (3 x+2)^2}{6655 \sqrt{1-2 x}}-\frac{6 \sqrt{1-2 x} (38025 x+114092)}{33275}-\frac{68 \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )}{33275 \sqrt{55}} \]
Antiderivative was successfully verified.
[In] Int[(2 + 3*x)^5/((1 - 2*x)^(5/2)*(3 + 5*x)^2),x]
[Out]
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Rubi in Sympy [A] time = 25.1485, size = 105, normalized size = 0.88 \[ - \frac{\sqrt{- 2 x + 1} \left (10266750 x + 30804840\right )}{1497375} - \frac{68 \sqrt{55} \operatorname{atanh}{\left (\frac{\sqrt{55} \sqrt{- 2 x + 1}}{11} \right )}}{1830125} - \frac{38 \left (3 x + 2\right )^{3}}{1815 \sqrt{- 2 x + 1} \left (5 x + 3\right )} - \frac{7588 \left (3 x + 2\right )^{2}}{6655 \sqrt{- 2 x + 1}} + \frac{7 \left (3 x + 2\right )^{4}}{33 \left (- 2 x + 1\right )^{\frac{3}{2}} \left (5 x + 3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**5/(1-2*x)**(5/2)/(3+5*x)**2,x)
[Out]
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Mathematica [A] time = 0.172076, size = 68, normalized size = 0.57 \[ \frac{-\frac{55 \left (1617165 x^4+16171650 x^3-28677318 x^2-10671002 x+7204728\right )}{(1-2 x)^{3/2} (5 x+3)}-204 \sqrt{55} \tanh ^{-1}\left (\sqrt{\frac{5}{11}} \sqrt{1-2 x}\right )}{5490375} \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 3*x)^5/((1 - 2*x)^(5/2)*(3 + 5*x)^2),x]
[Out]
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Maple [A] time = 0.021, size = 72, normalized size = 0.6 \[{\frac{81}{200} \left ( 1-2\,x \right ) ^{{\frac{3}{2}}}}-{\frac{8829}{1000}\sqrt{1-2\,x}}+{\frac{16807}{2904} \left ( 1-2\,x \right ) ^{-{\frac{3}{2}}}}-{\frac{228095}{10648}{\frac{1}{\sqrt{1-2\,x}}}}+{\frac{2}{831875}\sqrt{1-2\,x} \left ( -{\frac{6}{5}}-2\,x \right ) ^{-1}}-{\frac{68\,\sqrt{55}}{1830125}{\it Artanh} \left ({\frac{\sqrt{55}}{11}\sqrt{1-2\,x}} \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^5/(1-2*x)^(5/2)/(3+5*x)^2,x)
[Out]
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Maxima [A] time = 1.50984, size = 124, normalized size = 1.03 \[ \frac{81}{200} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{34}{1830125} \, \sqrt{55} \log \left (-\frac{\sqrt{55} - 5 \, \sqrt{-2 \, x + 1}}{\sqrt{55} + 5 \, \sqrt{-2 \, x + 1}}\right ) - \frac{8829}{1000} \, \sqrt{-2 \, x + 1} - \frac{427678077 \,{\left (2 \, x - 1\right )}^{2} + 2112880000 \, x - 802234125}{3993000 \,{\left (5 \,{\left (-2 \, x + 1\right )}^{\frac{5}{2}} - 11 \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^5/((5*x + 3)^2*(-2*x + 1)^(5/2)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.219455, size = 124, normalized size = 1.03 \[ \frac{\sqrt{55}{\left (102 \,{\left (10 \, x^{2} + x - 3\right )} \sqrt{-2 \, x + 1} \log \left (\frac{\sqrt{55}{\left (5 \, x - 8\right )} + 55 \, \sqrt{-2 \, x + 1}}{5 \, x + 3}\right ) + \sqrt{55}{\left (1617165 \, x^{4} + 16171650 \, x^{3} - 28677318 \, x^{2} - 10671002 \, x + 7204728\right )}\right )}}{5490375 \,{\left (10 \, x^{2} + x - 3\right )} \sqrt{-2 \, x + 1}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^5/((5*x + 3)^2*(-2*x + 1)^(5/2)),x, algorithm="fricas")
[Out]
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Sympy [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**5/(1-2*x)**(5/2)/(3+5*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.217242, size = 128, normalized size = 1.07 \[ \frac{81}{200} \,{\left (-2 \, x + 1\right )}^{\frac{3}{2}} + \frac{34}{1830125} \, \sqrt{55}{\rm ln}\left (\frac{{\left | -2 \, \sqrt{55} + 10 \, \sqrt{-2 \, x + 1} \right |}}{2 \,{\left (\sqrt{55} + 5 \, \sqrt{-2 \, x + 1}\right )}}\right ) - \frac{8829}{1000} \, \sqrt{-2 \, x + 1} - \frac{2401 \,{\left (285 \, x - 104\right )}}{15972 \,{\left (2 \, x - 1\right )} \sqrt{-2 \, x + 1}} - \frac{\sqrt{-2 \, x + 1}}{166375 \,{\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^5/((5*x + 3)^2*(-2*x + 1)^(5/2)),x, algorithm="giac")
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