Optimal. Leaf size=98 \[ \frac{13 \sqrt{\frac{3}{22}} \sqrt{5-2 x} F\left (\sin ^{-1}\left (\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right )|\frac{1}{3}\right )}{\sqrt{2 x-5}}-\frac{5 \sqrt{11} \sqrt{2 x-5} E\left (\sin ^{-1}\left (\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right )|-\frac{1}{2}\right )}{6 \sqrt{5-2 x}} \]
[Out]
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Rubi [A] time = 0.252159, antiderivative size = 98, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 5, integrand size = 33, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.152 \[ \frac{13 \sqrt{\frac{3}{22}} \sqrt{5-2 x} F\left (\sin ^{-1}\left (\sqrt{\frac{3}{11}} \sqrt{4 x+1}\right )|\frac{1}{3}\right )}{\sqrt{2 x-5}}-\frac{5 \sqrt{11} \sqrt{2 x-5} E\left (\sin ^{-1}\left (\frac{2 \sqrt{2-3 x}}{\sqrt{11}}\right )|-\frac{1}{2}\right )}{6 \sqrt{5-2 x}} \]
Antiderivative was successfully verified.
[In] Int[(7 + 5*x)/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]
[Out]
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Rubi in Sympy [A] time = 22.2094, size = 141, normalized size = 1.44 \[ - \frac{5 \sqrt{11} \sqrt{\frac{12 x}{11} + \frac{3}{11}} \sqrt{2 x - 5} E\left (\operatorname{asin}{\left (\frac{2 \sqrt{11} \sqrt{- 3 x + 2}}{11} \right )}\middle | - \frac{1}{2}\right )}{6 \sqrt{- \frac{6 x}{11} + \frac{15}{11}} \sqrt{4 x + 1}} + \frac{13 \sqrt{33} \sqrt{- \frac{12 x}{11} + \frac{8}{11}} \sqrt{- \frac{4 x}{11} + \frac{10}{11}} F\left (\operatorname{asin}{\left (\frac{\sqrt{33} \sqrt{4 x + 1}}{11} \right )}\middle | \frac{1}{3}\right )}{4 \sqrt{- 3 x + 2} \sqrt{2 x - 5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((7+5*x)/(2-3*x)**(1/2)/(-5+2*x)**(1/2)/(1+4*x)**(1/2),x)
[Out]
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Mathematica [A] time = 0.725348, size = 187, normalized size = 1.91 \[ \frac{220 \left (6 x^2-19 x+10\right ) \sqrt{4 x+1}-124 \sqrt{22} \sqrt{\frac{2 x-5}{4 x+1}} \sqrt{\frac{3 x-2}{4 x+1}} (4 x+1)^2 F\left (\left .\sin ^{-1}\left (\frac{\sqrt{\frac{11}{3}}}{\sqrt{4 x+1}}\right )\right |3\right )+55 \sqrt{22} \sqrt{\frac{2 x-5}{4 x+1}} \sqrt{\frac{3 x-2}{4 x+1}} (4 x+1)^2 E\left (\left .\sin ^{-1}\left (\frac{\sqrt{\frac{11}{3}}}{\sqrt{4 x+1}}\right )\right |3\right )}{132 \sqrt{2-3 x} \sqrt{2 x-5} (4 x+1)} \]
Antiderivative was successfully verified.
[In] Integrate[(7 + 5*x)/(Sqrt[2 - 3*x]*Sqrt[-5 + 2*x]*Sqrt[1 + 4*x]),x]
[Out]
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Maple [A] time = 0.021, size = 63, normalized size = 0.6 \[ -{\frac{\sqrt{11}}{66} \left ( 117\,{\it EllipticF} \left ( 2/11\,\sqrt{2-3\,x}\sqrt{11},i/2\sqrt{2} \right ) -55\,{\it EllipticE} \left ( 2/11\,\sqrt{2-3\,x}\sqrt{11},i/2\sqrt{2} \right ) \right ) \sqrt{5-2\,x}{\frac{1}{\sqrt{-5+2\,x}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((7+5*x)/(2-3*x)^(1/2)/(-5+2*x)^(1/2)/(1+4*x)^(1/2),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{5 \, x + 7}{\sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 7)/(sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{5 \, x + 7}{\sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 7)/(sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{5 x + 7}{\sqrt{- 3 x + 2} \sqrt{2 x - 5} \sqrt{4 x + 1}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((7+5*x)/(2-3*x)**(1/2)/(-5+2*x)**(1/2)/(1+4*x)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{5 \, x + 7}{\sqrt{4 \, x + 1} \sqrt{2 \, x - 5} \sqrt{-3 \, x + 2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((5*x + 7)/(sqrt(4*x + 1)*sqrt(2*x - 5)*sqrt(-3*x + 2)),x, algorithm="giac")
[Out]