Optimal. Leaf size=156 \[ \frac{7 (3 x+2)^{5/2}}{33 (1-2 x)^{3/2} \sqrt{5 x+3}}-\frac{434 (3 x+2)^{3/2}}{363 \sqrt{1-2 x} \sqrt{5 x+3}}+\frac{2129 \sqrt{1-2 x} \sqrt{3 x+2}}{19965 \sqrt{5 x+3}}-\frac{2252 F\left (\sin ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )|\frac{35}{33}\right )}{3025 \sqrt{33}}-\frac{148831 E\left (\sin ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )|\frac{35}{33}\right )}{6050 \sqrt{33}} \]
[Out]
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Rubi [A] time = 0.337265, antiderivative size = 156, normalized size of antiderivative = 1., number of steps used = 6, number of rules used = 5, integrand size = 28, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.179 \[ \frac{7 (3 x+2)^{5/2}}{33 (1-2 x)^{3/2} \sqrt{5 x+3}}-\frac{434 (3 x+2)^{3/2}}{363 \sqrt{1-2 x} \sqrt{5 x+3}}+\frac{2129 \sqrt{1-2 x} \sqrt{3 x+2}}{19965 \sqrt{5 x+3}}-\frac{2252 F\left (\sin ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )|\frac{35}{33}\right )}{3025 \sqrt{33}}-\frac{148831 E\left (\sin ^{-1}\left (\sqrt{\frac{3}{7}} \sqrt{1-2 x}\right )|\frac{35}{33}\right )}{6050 \sqrt{33}} \]
Antiderivative was successfully verified.
[In] Int[(2 + 3*x)^(7/2)/((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)),x]
[Out]
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Rubi in Sympy [A] time = 31.0929, size = 143, normalized size = 0.92 \[ \frac{2129 \sqrt{- 2 x + 1} \sqrt{3 x + 2}}{19965 \sqrt{5 x + 3}} - \frac{148831 \sqrt{33} E\left (\operatorname{asin}{\left (\frac{\sqrt{21} \sqrt{- 2 x + 1}}{7} \right )}\middle | \frac{35}{33}\right )}{199650} - \frac{2252 \sqrt{35} F\left (\operatorname{asin}{\left (\frac{\sqrt{55} \sqrt{- 2 x + 1}}{11} \right )}\middle | \frac{33}{35}\right )}{105875} - \frac{434 \left (3 x + 2\right )^{\frac{3}{2}}}{363 \sqrt{- 2 x + 1} \sqrt{5 x + 3}} + \frac{7 \left (3 x + 2\right )^{\frac{5}{2}}}{33 \left (- 2 x + 1\right )^{\frac{3}{2}} \sqrt{5 x + 3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**(7/2)/(1-2*x)**(5/2)/(3+5*x)**(3/2),x)
[Out]
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Mathematica [A] time = 0.337097, size = 97, normalized size = 0.62 \[ \frac{\frac{5 \sqrt{6 x+4} \left (189851 x^2+66174 x-28671\right )}{(1-2 x)^{3/2} \sqrt{5 x+3}}-74515 F\left (\sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )|-\frac{33}{2}\right )+148831 E\left (\sin ^{-1}\left (\sqrt{\frac{2}{11}} \sqrt{5 x+3}\right )|-\frac{33}{2}\right )}{99825 \sqrt{2}} \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 3*x)^(7/2)/((1 - 2*x)^(5/2)*(3 + 5*x)^(3/2)),x]
[Out]
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Maple [C] time = 0.034, size = 276, normalized size = 1.8 \[{\frac{1}{ \left ( 2994750\,{x}^{2}+3793350\,x+1197900 \right ) \left ( -1+2\,x \right ) ^{2}}\sqrt{1-2\,x}\sqrt{2+3\,x}\sqrt{3+5\,x} \left ( 149030\,\sqrt{2}{\it EllipticF} \left ( 1/11\,\sqrt{11}\sqrt{2}\sqrt{3+5\,x},i/2\sqrt{11}\sqrt{3}\sqrt{2} \right ) x\sqrt{3+5\,x}\sqrt{2+3\,x}\sqrt{1-2\,x}-297662\,\sqrt{2}{\it EllipticE} \left ( 1/11\,\sqrt{11}\sqrt{2}\sqrt{3+5\,x},i/2\sqrt{11}\sqrt{3}\sqrt{2} \right ) x\sqrt{3+5\,x}\sqrt{2+3\,x}\sqrt{1-2\,x}-74515\,\sqrt{2}\sqrt{3+5\,x}\sqrt{2+3\,x}\sqrt{1-2\,x}{\it EllipticF} \left ( 1/11\,\sqrt{11}\sqrt{2}\sqrt{3+5\,x},i/2\sqrt{11}\sqrt{3}\sqrt{2} \right ) +148831\,\sqrt{2}\sqrt{3+5\,x}\sqrt{2+3\,x}\sqrt{1-2\,x}{\it EllipticE} \left ( 1/11\,\sqrt{11}\sqrt{2}\sqrt{3+5\,x},i/2\sqrt{11}\sqrt{3}\sqrt{2} \right ) +5695530\,{x}^{3}+5782240\,{x}^{2}+463350\,x-573420 \right ) } \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^(7/2)/(1-2*x)^(5/2)/(3+5*x)^(3/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (3 \, x + 2\right )}^{\frac{7}{2}}}{{\left (5 \, x + 3\right )}^{\frac{3}{2}}{\left (-2 \, x + 1\right )}^{\frac{5}{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^(7/2)/((5*x + 3)^(3/2)*(-2*x + 1)^(5/2)),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \sqrt{3 \, x + 2}}{{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )} \sqrt{5 \, x + 3} \sqrt{-2 \, x + 1}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^(7/2)/((5*x + 3)^(3/2)*(-2*x + 1)^(5/2)),x, algorithm="fricas")
[Out]
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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((2+3*x)**(7/2)/(1-2*x)**(5/2)/(3+5*x)**(3/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (3 \, x + 2\right )}^{\frac{7}{2}}}{{\left (5 \, x + 3\right )}^{\frac{3}{2}}{\left (-2 \, x + 1\right )}^{\frac{5}{2}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^(7/2)/((5*x + 3)^(3/2)*(-2*x + 1)^(5/2)),x, algorithm="giac")
[Out]