Optimal. Leaf size=73 \[ -\frac{2 a^2 A}{5 x^{5/2}}-\frac{2 a^2 B}{3 x^{3/2}}-\frac{4 a A c}{\sqrt{x}}+4 a B c \sqrt{x}+\frac{2}{3} A c^2 x^{3/2}+\frac{2}{5} B c^2 x^{5/2} \]
[Out]
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Rubi [A] time = 0.0713917, antiderivative size = 73, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ -\frac{2 a^2 A}{5 x^{5/2}}-\frac{2 a^2 B}{3 x^{3/2}}-\frac{4 a A c}{\sqrt{x}}+4 a B c \sqrt{x}+\frac{2}{3} A c^2 x^{3/2}+\frac{2}{5} B c^2 x^{5/2} \]
Antiderivative was successfully verified.
[In] Int[((A + B*x)*(a + c*x^2)^2)/x^(7/2),x]
[Out]
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Rubi in Sympy [A] time = 8.70378, size = 76, normalized size = 1.04 \[ - \frac{2 A a^{2}}{5 x^{\frac{5}{2}}} - \frac{4 A a c}{\sqrt{x}} + \frac{2 A c^{2} x^{\frac{3}{2}}}{3} - \frac{2 B a^{2}}{3 x^{\frac{3}{2}}} + 4 B a c \sqrt{x} + \frac{2 B c^{2} x^{\frac{5}{2}}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x+A)*(c*x**2+a)**2/x**(7/2),x)
[Out]
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Mathematica [A] time = 0.0363424, size = 53, normalized size = 0.73 \[ \frac{-2 a^2 (3 A+5 B x)+60 a c x^2 (B x-A)+2 c^2 x^4 (5 A+3 B x)}{15 x^{5/2}} \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x)*(a + c*x^2)^2)/x^(7/2),x]
[Out]
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Maple [A] time = 0.009, size = 54, normalized size = 0.7 \[ -{\frac{-6\,B{c}^{2}{x}^{5}-10\,A{c}^{2}{x}^{4}-60\,aBc{x}^{3}+60\,aAc{x}^{2}+10\,{a}^{2}Bx+6\,A{a}^{2}}{15}{x}^{-{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x+A)*(c*x^2+a)^2/x^(7/2),x)
[Out]
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Maxima [A] time = 0.683973, size = 73, normalized size = 1. \[ \frac{2}{5} \, B c^{2} x^{\frac{5}{2}} + \frac{2}{3} \, A c^{2} x^{\frac{3}{2}} + 4 \, B a c \sqrt{x} - \frac{2 \,{\left (30 \, A a c x^{2} + 5 \, B a^{2} x + 3 \, A a^{2}\right )}}{15 \, x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)^2*(B*x + A)/x^(7/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.277405, size = 72, normalized size = 0.99 \[ \frac{2 \,{\left (3 \, B c^{2} x^{5} + 5 \, A c^{2} x^{4} + 30 \, B a c x^{3} - 30 \, A a c x^{2} - 5 \, B a^{2} x - 3 \, A a^{2}\right )}}{15 \, x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)^2*(B*x + A)/x^(7/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 7.33949, size = 76, normalized size = 1.04 \[ - \frac{2 A a^{2}}{5 x^{\frac{5}{2}}} - \frac{4 A a c}{\sqrt{x}} + \frac{2 A c^{2} x^{\frac{3}{2}}}{3} - \frac{2 B a^{2}}{3 x^{\frac{3}{2}}} + 4 B a c \sqrt{x} + \frac{2 B c^{2} x^{\frac{5}{2}}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x+A)*(c*x**2+a)**2/x**(7/2),x)
[Out]
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GIAC/XCAS [A] time = 0.266755, size = 73, normalized size = 1. \[ \frac{2}{5} \, B c^{2} x^{\frac{5}{2}} + \frac{2}{3} \, A c^{2} x^{\frac{3}{2}} + 4 \, B a c \sqrt{x} - \frac{2 \,{\left (30 \, A a c x^{2} + 5 \, B a^{2} x + 3 \, A a^{2}\right )}}{15 \, x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + a)^2*(B*x + A)/x^(7/2),x, algorithm="giac")
[Out]