Optimal. Leaf size=49 \[ -\frac{2 a^2}{5 d (d x)^{5/2}}-\frac{4 a b}{d^3 \sqrt{d x}}+\frac{2 b^2 (d x)^{3/2}}{3 d^5} \]
[Out]
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Rubi [A] time = 0.0374636, antiderivative size = 49, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 26, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.038 \[ -\frac{2 a^2}{5 d (d x)^{5/2}}-\frac{4 a b}{d^3 \sqrt{d x}}+\frac{2 b^2 (d x)^{3/2}}{3 d^5} \]
Antiderivative was successfully verified.
[In] Int[(a^2 + 2*a*b*x^2 + b^2*x^4)/(d*x)^(7/2),x]
[Out]
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Rubi in Sympy [A] time = 15.609, size = 46, normalized size = 0.94 \[ - \frac{2 a^{2}}{5 d \left (d x\right )^{\frac{5}{2}}} - \frac{4 a b}{d^{3} \sqrt{d x}} + \frac{2 b^{2} \left (d x\right )^{\frac{3}{2}}}{3 d^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b**2*x**4+2*a*b*x**2+a**2)/(d*x)**(7/2),x)
[Out]
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Mathematica [A] time = 0.0196514, size = 38, normalized size = 0.78 \[ \frac{2 \sqrt{d x} \left (-3 a^2-30 a b x^2+5 b^2 x^4\right )}{15 d^4 x^3} \]
Antiderivative was successfully verified.
[In] Integrate[(a^2 + 2*a*b*x^2 + b^2*x^4)/(d*x)^(7/2),x]
[Out]
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Maple [A] time = 0.01, size = 30, normalized size = 0.6 \[ -{\frac{ \left ( -10\,{b}^{2}{x}^{4}+60\,ab{x}^{2}+6\,{a}^{2} \right ) x}{15} \left ( dx \right ) ^{-{\frac{7}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b^2*x^4+2*a*b*x^2+a^2)/(d*x)^(7/2),x)
[Out]
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Maxima [A] time = 0.685156, size = 63, normalized size = 1.29 \[ \frac{2 \,{\left (\frac{5 \, \left (d x\right )^{\frac{3}{2}} b^{2}}{d^{4}} - \frac{3 \,{\left (10 \, a b d^{2} x^{2} + a^{2} d^{2}\right )}}{\left (d x\right )^{\frac{5}{2}} d^{2}}\right )}}{15 \, d} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^4 + 2*a*b*x^2 + a^2)/(d*x)^(7/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.256631, size = 46, normalized size = 0.94 \[ \frac{2 \,{\left (5 \, b^{2} x^{4} - 30 \, a b x^{2} - 3 \, a^{2}\right )}}{15 \, \sqrt{d x} d^{3} x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^4 + 2*a*b*x^2 + a^2)/(d*x)^(7/2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 6.84073, size = 48, normalized size = 0.98 \[ - \frac{2 a^{2}}{5 d^{\frac{7}{2}} x^{\frac{5}{2}}} - \frac{4 a b}{d^{\frac{7}{2}} \sqrt{x}} + \frac{2 b^{2} x^{\frac{3}{2}}}{3 d^{\frac{7}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b**2*x**4+2*a*b*x**2+a**2)/(d*x)**(7/2),x)
[Out]
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GIAC/XCAS [A] time = 0.262285, size = 65, normalized size = 1.33 \[ \frac{2 \,{\left (5 \, \sqrt{d x} b^{2} x - \frac{3 \,{\left (10 \, a b d^{3} x^{2} + a^{2} d^{3}\right )}}{\sqrt{d x} d^{2} x^{2}}\right )}}{15 \, d^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b^2*x^4 + 2*a*b*x^2 + a^2)/(d*x)^(7/2),x, algorithm="giac")
[Out]