Optimal. Leaf size=107 \[ -\frac{2 a^4 A}{5 x^{5/2}}-\frac{2 a^3 (a B+4 A b)}{3 x^{3/2}}-\frac{4 a^2 b (2 a B+3 A b)}{\sqrt{x}}+\frac{2}{3} b^3 x^{3/2} (4 a B+A b)+4 a b^2 \sqrt{x} (3 a B+2 A b)+\frac{2}{5} b^4 B x^{5/2} \]
[Out]
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Rubi [A] time = 0.132965, antiderivative size = 107, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 29, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.069 \[ -\frac{2 a^4 A}{5 x^{5/2}}-\frac{2 a^3 (a B+4 A b)}{3 x^{3/2}}-\frac{4 a^2 b (2 a B+3 A b)}{\sqrt{x}}+\frac{2}{3} b^3 x^{3/2} (4 a B+A b)+4 a b^2 \sqrt{x} (3 a B+2 A b)+\frac{2}{5} b^4 B x^{5/2} \]
Antiderivative was successfully verified.
[In] Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/x^(7/2),x]
[Out]
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Rubi in Sympy [A] time = 31.5246, size = 110, normalized size = 1.03 \[ - \frac{2 A a^{4}}{5 x^{\frac{5}{2}}} + \frac{2 B b^{4} x^{\frac{5}{2}}}{5} - \frac{2 a^{3} \left (4 A b + B a\right )}{3 x^{\frac{3}{2}}} - \frac{4 a^{2} b \left (3 A b + 2 B a\right )}{\sqrt{x}} + 4 a b^{2} \sqrt{x} \left (2 A b + 3 B a\right ) + \frac{2 b^{3} x^{\frac{3}{2}} \left (A b + 4 B a\right )}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2/x**(7/2),x)
[Out]
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Mathematica [A] time = 0.0503144, size = 85, normalized size = 0.79 \[ \frac{2 \left (a^4 (-(3 A+5 B x))-20 a^3 b x (A+3 B x)+90 a^2 b^2 x^2 (B x-A)+20 a b^3 x^3 (3 A+B x)+b^4 x^4 (5 A+3 B x)\right )}{15 x^{5/2}} \]
Antiderivative was successfully verified.
[In] Integrate[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/x^(7/2),x]
[Out]
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Maple [A] time = 0.011, size = 100, normalized size = 0.9 \[ -{\frac{-6\,{b}^{4}B{x}^{5}-10\,A{b}^{4}{x}^{4}-40\,B{x}^{4}a{b}^{3}-120\,aA{b}^{3}{x}^{3}-180\,B{x}^{3}{a}^{2}{b}^{2}+180\,{a}^{2}A{b}^{2}{x}^{2}+120\,B{x}^{2}{a}^{3}b+40\,{a}^{3}Abx+10\,{a}^{4}Bx+6\,A{a}^{4}}{15}{x}^{-{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((B*x+A)*(b^2*x^2+2*a*b*x+a^2)^2/x^(7/2),x)
[Out]
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Maxima [A] time = 0.689886, size = 135, normalized size = 1.26 \[ \frac{2}{5} \, B b^{4} x^{\frac{5}{2}} + \frac{2}{3} \,{\left (4 \, B a b^{3} + A b^{4}\right )} x^{\frac{3}{2}} + 4 \,{\left (3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right )} \sqrt{x} - \frac{2 \,{\left (3 \, A a^{4} + 30 \,{\left (2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right )} x^{2} + 5 \,{\left (B a^{4} + 4 \, A a^{3} b\right )} x\right )}}{15 \, x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^2 + 2*a*b*x + a^2)^2*(B*x + A)/x^(7/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.31227, size = 134, normalized size = 1.25 \[ \frac{2 \,{\left (3 \, B b^{4} x^{5} - 3 \, A a^{4} + 5 \,{\left (4 \, B a b^{3} + A b^{4}\right )} x^{4} + 30 \,{\left (3 \, B a^{2} b^{2} + 2 \, A a b^{3}\right )} x^{3} - 30 \,{\left (2 \, B a^{3} b + 3 \, A a^{2} b^{2}\right )} x^{2} - 5 \,{\left (B a^{4} + 4 \, A a^{3} b\right )} x\right )}}{15 \, x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^2 + 2*a*b*x + a^2)^2*(B*x + A)/x^(7/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 9.26062, size = 141, normalized size = 1.32 \[ - \frac{2 A a^{4}}{5 x^{\frac{5}{2}}} - \frac{8 A a^{3} b}{3 x^{\frac{3}{2}}} - \frac{12 A a^{2} b^{2}}{\sqrt{x}} + 8 A a b^{3} \sqrt{x} + \frac{2 A b^{4} x^{\frac{3}{2}}}{3} - \frac{2 B a^{4}}{3 x^{\frac{3}{2}}} - \frac{8 B a^{3} b}{\sqrt{x}} + 12 B a^{2} b^{2} \sqrt{x} + \frac{8 B a b^{3} x^{\frac{3}{2}}}{3} + \frac{2 B b^{4} x^{\frac{5}{2}}}{5} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x+A)*(b**2*x**2+2*a*b*x+a**2)**2/x**(7/2),x)
[Out]
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GIAC/XCAS [A] time = 0.272007, size = 135, normalized size = 1.26 \[ \frac{2}{5} \, B b^{4} x^{\frac{5}{2}} + \frac{8}{3} \, B a b^{3} x^{\frac{3}{2}} + \frac{2}{3} \, A b^{4} x^{\frac{3}{2}} + 12 \, B a^{2} b^{2} \sqrt{x} + 8 \, A a b^{3} \sqrt{x} - \frac{2 \,{\left (60 \, B a^{3} b x^{2} + 90 \, A a^{2} b^{2} x^{2} + 5 \, B a^{4} x + 20 \, A a^{3} b x + 3 \, A a^{4}\right )}}{15 \, x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^2 + 2*a*b*x + a^2)^2*(B*x + A)/x^(7/2),x, algorithm="giac")
[Out]