Optimal. Leaf size=44 \[ \frac{c \left (a+c x^4\right )^{5/2}}{35 a^2 x^{10}}-\frac{\left (a+c x^4\right )^{5/2}}{14 a x^{14}} \]
[Out]
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Rubi [A] time = 0.0404651, antiderivative size = 44, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133 \[ \frac{c \left (a+c x^4\right )^{5/2}}{35 a^2 x^{10}}-\frac{\left (a+c x^4\right )^{5/2}}{14 a x^{14}} \]
Antiderivative was successfully verified.
[In] Int[(a + c*x^4)^(3/2)/x^15,x]
[Out]
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Rubi in Sympy [A] time = 4.27583, size = 36, normalized size = 0.82 \[ - \frac{\left (a + c x^{4}\right )^{\frac{5}{2}}}{14 a x^{14}} + \frac{c \left (a + c x^{4}\right )^{\frac{5}{2}}}{35 a^{2} x^{10}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**4+a)**(3/2)/x**15,x)
[Out]
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Mathematica [A] time = 0.0400296, size = 31, normalized size = 0.7 \[ \frac{\left (a+c x^4\right )^{5/2} \left (2 c x^4-5 a\right )}{70 a^2 x^{14}} \]
Antiderivative was successfully verified.
[In] Integrate[(a + c*x^4)^(3/2)/x^15,x]
[Out]
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Maple [A] time = 0.007, size = 28, normalized size = 0.6 \[ -{\frac{-2\,c{x}^{4}+5\,a}{70\,{x}^{14}{a}^{2}} \left ( c{x}^{4}+a \right ) ^{{\frac{5}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^4+a)^(3/2)/x^15,x)
[Out]
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Maxima [A] time = 1.42321, size = 47, normalized size = 1.07 \[ \frac{\frac{7 \,{\left (c x^{4} + a\right )}^{\frac{5}{2}} c}{x^{10}} - \frac{5 \,{\left (c x^{4} + a\right )}^{\frac{7}{2}}}{x^{14}}}{70 \, a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)^(3/2)/x^15,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.290969, size = 66, normalized size = 1.5 \[ \frac{{\left (2 \, c^{3} x^{12} - a c^{2} x^{8} - 8 \, a^{2} c x^{4} - 5 \, a^{3}\right )} \sqrt{c x^{4} + a}}{70 \, a^{2} x^{14}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)^(3/2)/x^15,x, algorithm="fricas")
[Out]
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Sympy [A] time = 18.5229, size = 92, normalized size = 2.09 \[ - \frac{a \sqrt{c} \sqrt{\frac{a}{c x^{4}} + 1}}{14 x^{12}} - \frac{4 c^{\frac{3}{2}} \sqrt{\frac{a}{c x^{4}} + 1}}{35 x^{8}} - \frac{c^{\frac{5}{2}} \sqrt{\frac{a}{c x^{4}} + 1}}{70 a x^{4}} + \frac{c^{\frac{7}{2}} \sqrt{\frac{a}{c x^{4}} + 1}}{35 a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**4+a)**(3/2)/x**15,x)
[Out]
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GIAC/XCAS [A] time = 0.218721, size = 105, normalized size = 2.39 \[ -\frac{\frac{7 \,{\left (3 \,{\left (c + \frac{a}{x^{4}}\right )}^{\frac{5}{2}} - 5 \,{\left (c + \frac{a}{x^{4}}\right )}^{\frac{3}{2}} c\right )} c}{a} + \frac{15 \,{\left (c + \frac{a}{x^{4}}\right )}^{\frac{7}{2}} - 42 \,{\left (c + \frac{a}{x^{4}}\right )}^{\frac{5}{2}} c + 35 \,{\left (c + \frac{a}{x^{4}}\right )}^{\frac{3}{2}} c^{2}}{a}}{210 \, a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^4 + a)^(3/2)/x^15,x, algorithm="giac")
[Out]