Optimal. Leaf size=33 \[ \frac{2 i (a-i a x)^{5/4}}{5 a^2 (a+i a x)^{5/4}} \]
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Rubi [A] time = 0.0234605, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.04 \[ \frac{2 i (a-i a x)^{5/4}}{5 a^2 (a+i a x)^{5/4}} \]
Antiderivative was successfully verified.
[In] Int[(a - I*a*x)^(1/4)/(a + I*a*x)^(9/4),x]
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Rubi in Sympy [A] time = 5.88938, size = 27, normalized size = 0.82 \[ \frac{2 i \left (- i a x + a\right )^{\frac{5}{4}}}{5 a^{2} \left (i a x + a\right )^{\frac{5}{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((a-I*a*x)**(1/4)/(a+I*a*x)**(9/4),x)
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Mathematica [A] time = 0.0303027, size = 43, normalized size = 1.3 \[ -\frac{2 (x+i) \sqrt [4]{a-i a x} (a+i a x)^{3/4}}{5 a^3 (x-i)^2} \]
Antiderivative was successfully verified.
[In] Integrate[(a - I*a*x)^(1/4)/(a + I*a*x)^(9/4),x]
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Maple [B] time = 0.062, size = 50, normalized size = 1.5 \[{\frac{2\,{x}^{2}-2+4\,ix}{5\,{a}^{2} \left ( -1+ix \right ) \left ( x-i \right ) }\sqrt [4]{-a \left ( -1+ix \right ) }{\frac{1}{\sqrt [4]{a \left ( 1+ix \right ) }}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((a-I*a*x)^(1/4)/(a+I*a*x)^(9/4),x)
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (-i \, a x + a\right )}^{\frac{1}{4}}}{{\left (i \, a x + a\right )}^{\frac{9}{4}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-I*a*x + a)^(1/4)/(I*a*x + a)^(9/4),x, algorithm="maxima")
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Fricas [A] time = 0.225519, size = 61, normalized size = 1.85 \[ -\frac{{\left (i \, a x + a\right )}^{\frac{3}{4}}{\left (-i \, a x + a\right )}^{\frac{1}{4}}{\left (2 \, x + 2 i\right )}}{5 \, a^{3} x^{2} - 10 i \, a^{3} x - 5 \, a^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-I*a*x + a)^(1/4)/(I*a*x + a)^(9/4),x, algorithm="fricas")
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((a-I*a*x)**(1/4)/(a+I*a*x)**(9/4),x)
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GIAC/XCAS [A] time = 0.224942, size = 46, normalized size = 1.39 \[ -\frac{{\left (-i \, a x + a\right )}^{\frac{1}{4}}{\left (-\frac{4 i \, a}{i \, a x + a} + 2 i\right )}}{5 \,{\left (i \, a x + a\right )}^{\frac{1}{4}} a^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((-I*a*x + a)^(1/4)/(I*a*x + a)^(9/4),x, algorithm="giac")
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