Optimal. Leaf size=61 \[ -\frac{2 a^2 A}{5 x^{5/2}}+\frac{2}{3} b x^{3/2} (2 a B+A b)-\frac{2 a (a B+2 A b)}{\sqrt{x}}+\frac{2}{7} b^2 B x^{7/2} \]
[Out]
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Rubi [A] time = 0.0885723, antiderivative size = 61, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ -\frac{2 a^2 A}{5 x^{5/2}}+\frac{2}{3} b x^{3/2} (2 a B+A b)-\frac{2 a (a B+2 A b)}{\sqrt{x}}+\frac{2}{7} b^2 B x^{7/2} \]
Antiderivative was successfully verified.
[In] Int[((a + b*x^2)^2*(A + B*x^2))/x^(7/2),x]
[Out]
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Rubi in Sympy [A] time = 12.7748, size = 61, normalized size = 1. \[ - \frac{2 A a^{2}}{5 x^{\frac{5}{2}}} + \frac{2 B b^{2} x^{\frac{7}{2}}}{7} - \frac{2 a \left (2 A b + B a\right )}{\sqrt{x}} + \frac{2 b x^{\frac{3}{2}} \left (A b + 2 B a\right )}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)**2*(B*x**2+A)/x**(7/2),x)
[Out]
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Mathematica [A] time = 0.0289204, size = 57, normalized size = 0.93 \[ \frac{-42 a^2 \left (A+5 B x^2\right )+140 a b x^2 \left (B x^2-3 A\right )+10 b^2 x^4 \left (7 A+3 B x^2\right )}{105 x^{5/2}} \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x^2)^2*(A + B*x^2))/x^(7/2),x]
[Out]
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Maple [A] time = 0.009, size = 56, normalized size = 0.9 \[ -{\frac{-30\,{b}^{2}B{x}^{6}-70\,A{b}^{2}{x}^{4}-140\,{x}^{4}abB+420\,aAb{x}^{2}+210\,B{a}^{2}{x}^{2}+42\,{a}^{2}A}{105}{x}^{-{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)^2*(B*x^2+A)/x^(7/2),x)
[Out]
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Maxima [A] time = 1.32982, size = 72, normalized size = 1.18 \[ \frac{2}{7} \, B b^{2} x^{\frac{7}{2}} + \frac{2}{3} \,{\left (2 \, B a b + A b^{2}\right )} x^{\frac{3}{2}} - \frac{2 \,{\left (A a^{2} + 5 \,{\left (B a^{2} + 2 \, A a b\right )} x^{2}\right )}}{5 \, x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)^2/x^(7/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.218293, size = 72, normalized size = 1.18 \[ \frac{2 \,{\left (15 \, B b^{2} x^{6} + 35 \,{\left (2 \, B a b + A b^{2}\right )} x^{4} - 21 \, A a^{2} - 105 \,{\left (B a^{2} + 2 \, A a b\right )} x^{2}\right )}}{105 \, x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)^2/x^(7/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 15.4564, size = 76, normalized size = 1.25 \[ - \frac{2 A a^{2}}{5 x^{\frac{5}{2}}} - \frac{4 A a b}{\sqrt{x}} + \frac{2 A b^{2} x^{\frac{3}{2}}}{3} - \frac{2 B a^{2}}{\sqrt{x}} + \frac{4 B a b x^{\frac{3}{2}}}{3} + \frac{2 B b^{2} x^{\frac{7}{2}}}{7} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)**2*(B*x**2+A)/x**(7/2),x)
[Out]
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GIAC/XCAS [A] time = 0.212193, size = 74, normalized size = 1.21 \[ \frac{2}{7} \, B b^{2} x^{\frac{7}{2}} + \frac{4}{3} \, B a b x^{\frac{3}{2}} + \frac{2}{3} \, A b^{2} x^{\frac{3}{2}} - \frac{2 \,{\left (5 \, B a^{2} x^{2} + 10 \, A a b x^{2} + A a^{2}\right )}}{5 \, x^{\frac{5}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)^2/x^(7/2),x, algorithm="giac")
[Out]