Optimal. Leaf size=100 \[ \frac{16 i \sqrt [4]{a-i a x}}{15 a^4 \sqrt [4]{a+i a x}}+\frac{8 i \sqrt [4]{a-i a x}}{15 a^3 (a+i a x)^{5/4}}-\frac{2 i}{3 a^2 (a+i a x)^{5/4} (a-i a x)^{3/4}} \]
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Rubi [A] time = 0.0809503, antiderivative size = 100, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 25, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.08 \[ \frac{16 i \sqrt [4]{a-i a x}}{15 a^4 \sqrt [4]{a+i a x}}+\frac{8 i \sqrt [4]{a-i a x}}{15 a^3 (a+i a x)^{5/4}}-\frac{2 i}{3 a^2 (a+i a x)^{5/4} (a-i a x)^{3/4}} \]
Antiderivative was successfully verified.
[In] Int[1/((a - I*a*x)^(7/4)*(a + I*a*x)^(9/4)),x]
[Out]
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Rubi in Sympy [A] time = 16.575, size = 85, normalized size = 0.85 \[ \frac{2 i}{5 a^{2} \left (- i a x + a\right )^{\frac{3}{4}} \left (i a x + a\right )^{\frac{5}{4}}} + \frac{8 i}{5 a^{3} \left (- i a x + a\right )^{\frac{3}{4}} \sqrt [4]{i a x + a}} - \frac{16 i \left (i a x + a\right )^{\frac{3}{4}}}{15 a^{4} \left (- i a x + a\right )^{\frac{3}{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a-I*a*x)**(7/4)/(a+I*a*x)**(9/4),x)
[Out]
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Mathematica [A] time = 0.0519934, size = 52, normalized size = 0.52 \[ -\frac{2 i \left (8 x^2-4 i x+7\right ) (a+i a x)^{3/4}}{15 a^4 (x-i)^2 (a-i a x)^{3/4}} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a - I*a*x)^(7/4)*(a + I*a*x)^(9/4)),x]
[Out]
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Maple [A] time = 0.072, size = 44, normalized size = 0.4 \[{\frac{16\,{x}^{2}-8\,ix+14}{15\,{a}^{3} \left ( x-i \right ) } \left ( -a \left ( -1+ix \right ) \right ) ^{-{\frac{3}{4}}}{\frac{1}{\sqrt [4]{a \left ( 1+ix \right ) }}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a-I*a*x)^(7/4)/(a+I*a*x)^(9/4),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: RuntimeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((I*a*x + a)^(9/4)*(-I*a*x + a)^(7/4)),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.244274, size = 55, normalized size = 0.55 \[ \frac{2 \,{\left (8 \, x^{2} - 4 i \, x + 7\right )}}{15 \,{\left (a^{3} x - i \, a^{3}\right )}{\left (i \, a x + a\right )}^{\frac{1}{4}}{\left (-i \, a x + a\right )}^{\frac{3}{4}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((I*a*x + a)^(9/4)*(-I*a*x + a)^(7/4)),x, algorithm="fricas")
[Out]
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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(1/(a-I*a*x)**(7/4)/(a+I*a*x)**(9/4),x)
[Out]
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GIAC/XCAS [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((I*a*x + a)^(9/4)*(-I*a*x + a)^(7/4)),x, algorithm="giac")
[Out]