Optimal. Leaf size=53 \[ \frac{\left (a+b x^2\right )^{7/2} (2 A b-9 a B)}{63 a^2 x^7}-\frac{A \left (a+b x^2\right )^{7/2}}{9 a x^9} \]
[Out]
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Rubi [A] time = 0.083881, antiderivative size = 53, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ \frac{\left (a+b x^2\right )^{7/2} (2 A b-9 a B)}{63 a^2 x^7}-\frac{A \left (a+b x^2\right )^{7/2}}{9 a x^9} \]
Antiderivative was successfully verified.
[In] Int[((a + b*x^2)^(5/2)*(A + B*x^2))/x^10,x]
[Out]
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Rubi in Sympy [A] time = 9.31011, size = 46, normalized size = 0.87 \[ - \frac{A \left (a + b x^{2}\right )^{\frac{7}{2}}}{9 a x^{9}} + \frac{\left (a + b x^{2}\right )^{\frac{7}{2}} \left (2 A b - 9 B a\right )}{63 a^{2} x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2+a)**(5/2)*(B*x**2+A)/x**10,x)
[Out]
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Mathematica [A] time = 0.0888106, size = 40, normalized size = 0.75 \[ -\frac{\left (a+b x^2\right )^{7/2} \left (7 a A+9 a B x^2-2 A b x^2\right )}{63 a^2 x^9} \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x^2)^(5/2)*(A + B*x^2))/x^10,x]
[Out]
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Maple [A] time = 0.007, size = 37, normalized size = 0.7 \[ -{\frac{-2\,Ab{x}^{2}+9\,Ba{x}^{2}+7\,Aa}{63\,{x}^{9}{a}^{2}} \left ( b{x}^{2}+a \right ) ^{{\frac{7}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2+a)^(5/2)*(B*x^2+A)/x^10,x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)^(5/2)/x^10,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.322045, size = 138, normalized size = 2.6 \[ -\frac{{\left ({\left (9 \, B a b^{3} - 2 \, A b^{4}\right )} x^{8} +{\left (27 \, B a^{2} b^{2} + A a b^{3}\right )} x^{6} + 7 \, A a^{4} + 3 \,{\left (9 \, B a^{3} b + 5 \, A a^{2} b^{2}\right )} x^{4} +{\left (9 \, B a^{4} + 19 \, A a^{3} b\right )} x^{2}\right )} \sqrt{b x^{2} + a}}{63 \, a^{2} x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)^(5/2)/x^10,x, algorithm="fricas")
[Out]
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Sympy [A] time = 28.2878, size = 1489, normalized size = 28.09 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2+a)**(5/2)*(B*x**2+A)/x**10,x)
[Out]
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GIAC/XCAS [A] time = 0.269149, size = 616, normalized size = 11.62 \[ \frac{2 \,{\left (63 \,{\left (\sqrt{b} x - \sqrt{b x^{2} + a}\right )}^{16} B b^{\frac{7}{2}} - 126 \,{\left (\sqrt{b} x - \sqrt{b x^{2} + a}\right )}^{14} B a b^{\frac{7}{2}} + 126 \,{\left (\sqrt{b} x - \sqrt{b x^{2} + a}\right )}^{14} A b^{\frac{9}{2}} + 378 \,{\left (\sqrt{b} x - \sqrt{b x^{2} + a}\right )}^{12} B a^{2} b^{\frac{7}{2}} + 210 \,{\left (\sqrt{b} x - \sqrt{b x^{2} + a}\right )}^{12} A a b^{\frac{9}{2}} - 630 \,{\left (\sqrt{b} x - \sqrt{b x^{2} + a}\right )}^{10} B a^{3} b^{\frac{7}{2}} + 630 \,{\left (\sqrt{b} x - \sqrt{b x^{2} + a}\right )}^{10} A a^{2} b^{\frac{9}{2}} + 504 \,{\left (\sqrt{b} x - \sqrt{b x^{2} + a}\right )}^{8} B a^{4} b^{\frac{7}{2}} + 378 \,{\left (\sqrt{b} x - \sqrt{b x^{2} + a}\right )}^{8} A a^{3} b^{\frac{9}{2}} - 378 \,{\left (\sqrt{b} x - \sqrt{b x^{2} + a}\right )}^{6} B a^{5} b^{\frac{7}{2}} + 378 \,{\left (\sqrt{b} x - \sqrt{b x^{2} + a}\right )}^{6} A a^{4} b^{\frac{9}{2}} + 198 \,{\left (\sqrt{b} x - \sqrt{b x^{2} + a}\right )}^{4} B a^{6} b^{\frac{7}{2}} + 54 \,{\left (\sqrt{b} x - \sqrt{b x^{2} + a}\right )}^{4} A a^{5} b^{\frac{9}{2}} - 18 \,{\left (\sqrt{b} x - \sqrt{b x^{2} + a}\right )}^{2} B a^{7} b^{\frac{7}{2}} + 18 \,{\left (\sqrt{b} x - \sqrt{b x^{2} + a}\right )}^{2} A a^{6} b^{\frac{9}{2}} + 9 \, B a^{8} b^{\frac{7}{2}} - 2 \, A a^{7} b^{\frac{9}{2}}\right )}}{63 \,{\left ({\left (\sqrt{b} x - \sqrt{b x^{2} + a}\right )}^{2} - a\right )}^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x^2 + A)*(b*x^2 + a)^(5/2)/x^10,x, algorithm="giac")
[Out]