Optimal. Leaf size=249 \[ -\frac{4839325048 \sqrt{1-2 x} \sqrt{3 x+2}}{67110351 \sqrt{5 x+3}}+\frac{72709316 \sqrt{1-2 x}}{10168235 \sqrt{3 x+2} \sqrt{5 x+3}}+\frac{499564 \sqrt{1-2 x}}{1452605 (3 x+2)^{3/2} \sqrt{5 x+3}}-\frac{2206 \sqrt{1-2 x}}{207515 (3 x+2)^{5/2} \sqrt{5 x+3}}+\frac{1616}{17787 \sqrt{1-2 x} (3 x+2)^{5/2} \sqrt{5 x+3}}+\frac{4}{231 (1-2 x)^{3/2} (3 x+2)^{5/2} \sqrt{5 x+3}}+\frac{145418632 F\left (\sin ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )|\frac{35}{33}\right )}{10168235 \sqrt{33}}+\frac{4839325048 E\left (\sin ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )|\frac{35}{33}\right )}{10168235 \sqrt{33}} \]
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Rubi [A] time = 0.619701, antiderivative size = 249, normalized size of antiderivative = 1., number of steps used = 9, number of rules used = 5, integrand size = 28, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.179 \[ -\frac{4839325048 \sqrt{1-2 x} \sqrt{3 x+2}}{67110351 \sqrt{5 x+3}}+\frac{72709316 \sqrt{1-2 x}}{10168235 \sqrt{3 x+2} \sqrt{5 x+3}}+\frac{499564 \sqrt{1-2 x}}{1452605 (3 x+2)^{3/2} \sqrt{5 x+3}}-\frac{2206 \sqrt{1-2 x}}{207515 (3 x+2)^{5/2} \sqrt{5 x+3}}+\frac{1616}{17787 \sqrt{1-2 x} (3 x+2)^{5/2} \sqrt{5 x+3}}+\frac{4}{231 (1-2 x)^{3/2} (3 x+2)^{5/2} \sqrt{5 x+3}}+\frac{145418632 F\left (\sin ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )|\frac{35}{33}\right )}{10168235 \sqrt{33}}+\frac{4839325048 E\left (\sin ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )|\frac{35}{33}\right )}{10168235 \sqrt{33}} \]
Antiderivative was successfully verified.
[In] Int[1/((1 - 2*x)^(5/2)*(2 + 3*x)^(7/2)*(3 + 5*x)^(3/2)),x]
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Rubi in Sympy [A] time = 52.1771, size = 230, normalized size = 0.92 \[ \frac{4839325048 \sqrt{33} E\left (\operatorname{asin}{\left (\frac{\sqrt{21} \sqrt{- 2 x + 1}}{7} \right )}\middle | \frac{35}{33}\right )}{335551755} + \frac{145418632 \sqrt{33} F\left (\operatorname{asin}{\left (\frac{\sqrt{21} \sqrt{- 2 x + 1}}{7} \right )}\middle | \frac{35}{33}\right )}{335551755} + \frac{9678650096 \sqrt{3 x + 2} \sqrt{5 x + 3}}{335551755 \sqrt{- 2 x + 1}} - \frac{142421248 \sqrt{3 x + 2}}{871563 \sqrt{- 2 x + 1} \sqrt{5 x + 3}} + \frac{2173036}{132055 \sqrt{- 2 x + 1} \sqrt{3 x + 2} \sqrt{5 x + 3}} + \frac{15272}{18865 \sqrt{- 2 x + 1} \left (3 x + 2\right )^{\frac{3}{2}} \sqrt{5 x + 3}} + \frac{178}{2695 \sqrt{- 2 x + 1} \left (3 x + 2\right )^{\frac{5}{2}} \sqrt{5 x + 3}} + \frac{4}{231 \left (- 2 x + 1\right )^{\frac{3}{2}} \left (3 x + 2\right )^{\frac{5}{2}} \sqrt{5 x + 3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(1-2*x)**(5/2)/(2+3*x)**(7/2)/(3+5*x)**(3/2),x)
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Mathematica [A] time = 0.329322, size = 115, normalized size = 0.46 \[ \frac{2 \left (-\frac{1306617762960 x^5+1263428429256 x^4-559512908172 x^3-673871013766 x^2+53503915182 x+91855922241}{(1-2 x)^{3/2} (3 x+2)^{5/2} \sqrt{5 x+3}}-2 \sqrt{2} \left (1209831262 E\left (\sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )|-\frac{33}{2}\right )-609979405 F\left (\sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )|-\frac{33}{2}\right )\right )\right )}{335551755} \]
Antiderivative was successfully verified.
[In] Integrate[1/((1 - 2*x)^(5/2)*(2 + 3*x)^(7/2)*(3 + 5*x)^(3/2)),x]
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Maple [C] time = 0.043, size = 502, normalized size = 2. \[ -{\frac{2}{335551755\, \left ( -1+2\,x \right ) ^{2}}\sqrt{1-2\,x} \left ( 21959258580\,\sqrt{2}{\it EllipticF} \left ( 1/11\,\sqrt{11}\sqrt{2}\sqrt{3+5\,x},i/2\sqrt{11}\sqrt{3}\sqrt{2} \right ){x}^{3}\sqrt{1-2\,x}\sqrt{3+5\,x}\sqrt{2+3\,x}-43553925432\,\sqrt{2}{\it EllipticE} \left ( 1/11\,\sqrt{11}\sqrt{2}\sqrt{3+5\,x},i/2\sqrt{11}\sqrt{3}\sqrt{2} \right ){x}^{3}\sqrt{1-2\,x}\sqrt{3+5\,x}\sqrt{2+3\,x}+18299382150\,\sqrt{2}{\it EllipticF} \left ( 1/11\,\sqrt{11}\sqrt{2}\sqrt{3+5\,x},i/2\sqrt{11}\sqrt{3}\sqrt{2} \right ){x}^{2}\sqrt{3+5\,x}\sqrt{2+3\,x}\sqrt{1-2\,x}-36294937860\,\sqrt{2}{\it EllipticE} \left ( 1/11\,\sqrt{11}\sqrt{2}\sqrt{3+5\,x},i/2\sqrt{11}\sqrt{3}\sqrt{2} \right ){x}^{2}\sqrt{3+5\,x}\sqrt{2+3\,x}\sqrt{1-2\,x}-4879835240\,\sqrt{2}{\it EllipticF} \left ( 1/11\,\sqrt{11}\sqrt{2}\sqrt{3+5\,x},i/2\sqrt{11}\sqrt{3}\sqrt{2} \right ) x\sqrt{3+5\,x}\sqrt{2+3\,x}\sqrt{1-2\,x}+9678650096\,\sqrt{2}{\it EllipticE} \left ( 1/11\,\sqrt{11}\sqrt{2}\sqrt{3+5\,x},i/2\sqrt{11}\sqrt{3}\sqrt{2} \right ) x\sqrt{3+5\,x}\sqrt{2+3\,x}\sqrt{1-2\,x}-4879835240\,\sqrt{2}\sqrt{3+5\,x}\sqrt{2+3\,x}\sqrt{1-2\,x}{\it EllipticF} \left ( 1/11\,\sqrt{11}\sqrt{2}\sqrt{3+5\,x},i/2\sqrt{11}\sqrt{3}\sqrt{2} \right ) +9678650096\,\sqrt{2}\sqrt{3+5\,x}\sqrt{2+3\,x}\sqrt{1-2\,x}{\it EllipticE} \left ( 1/11\,\sqrt{11}\sqrt{2}\sqrt{3+5\,x},i/2\sqrt{11}\sqrt{3}\sqrt{2} \right ) +1306617762960\,{x}^{5}+1263428429256\,{x}^{4}-559512908172\,{x}^{3}-673871013766\,{x}^{2}+53503915182\,x+91855922241 \right ) \left ( 2+3\,x \right ) ^{-{\frac{5}{2}}}{\frac{1}{\sqrt{3+5\,x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(1-2*x)^(5/2)/(2+3*x)^(7/2)/(3+5*x)^(3/2),x)
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (5 \, x + 3\right )}^{\frac{3}{2}}{\left (3 \, x + 2\right )}^{\frac{7}{2}}{\left (-2 \, x + 1\right )}^{\frac{5}{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x + 3)^(3/2)*(3*x + 2)^(7/2)*(-2*x + 1)^(5/2)),x, algorithm="maxima")
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{1}{{\left (540 \, x^{6} + 864 \, x^{5} + 99 \, x^{4} - 425 \, x^{3} - 154 \, x^{2} + 52 \, x + 24\right )} \sqrt{5 \, x + 3} \sqrt{3 \, x + 2} \sqrt{-2 \, x + 1}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x + 3)^(3/2)*(3*x + 2)^(7/2)*(-2*x + 1)^(5/2)),x, algorithm="fricas")
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(1-2*x)**(5/2)/(2+3*x)**(7/2)/(3+5*x)**(3/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (5 \, x + 3\right )}^{\frac{3}{2}}{\left (3 \, x + 2\right )}^{\frac{7}{2}}{\left (-2 \, x + 1\right )}^{\frac{5}{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((5*x + 3)^(3/2)*(3*x + 2)^(7/2)*(-2*x + 1)^(5/2)),x, algorithm="giac")
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