Optimal. Leaf size=100 \[ -\frac{16 i \sqrt [4]{a+i a x}}{45 a^4 \sqrt [4]{a-i a x}}-\frac{8 i \sqrt [4]{a+i a x}}{45 a^3 (a-i a x)^{5/4}}-\frac{2 i \sqrt [4]{a+i a x}}{9 a^2 (a-i a x)^{9/4}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0809087, 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 \[ -\frac{16 i \sqrt [4]{a+i a x}}{45 a^4 \sqrt [4]{a-i a x}}-\frac{8 i \sqrt [4]{a+i a x}}{45 a^3 (a-i a x)^{5/4}}-\frac{2 i \sqrt [4]{a+i a x}}{9 a^2 (a-i a x)^{9/4}} \]
Antiderivative was successfully verified.
[In] Int[1/((a - I*a*x)^(13/4)*(a + I*a*x)^(3/4)),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 18.3032, size = 87, normalized size = 0.87 \[ - \frac{2 i \sqrt [4]{i a x + a}}{9 a^{2} \left (- i a x + a\right )^{\frac{9}{4}}} - \frac{8 i \sqrt [4]{i a x + a}}{45 a^{3} \left (- i a x + a\right )^{\frac{5}{4}}} - \frac{16 i \sqrt [4]{i a x + a}}{45 a^{4} \sqrt [4]{- i a x + a}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a-I*a*x)**(13/4)/(a+I*a*x)**(3/4),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0497746, size = 52, normalized size = 0.52 \[ \frac{2 \left (-8 i x^2+20 x+17 i\right ) \sqrt [4]{a+i a x}}{45 a^4 (x+i)^2 \sqrt [4]{a-i a x}} \]
Antiderivative was successfully verified.
[In] Integrate[1/((a - I*a*x)^(13/4)*(a + I*a*x)^(3/4)),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.065, size = 50, normalized size = 0.5 \[{\frac{24\,i{x}^{2}+16\,{x}^{3}+6\,x+34\,i}{45\,{a}^{3} \left ( x+i \right ) ^{2}} \left ( a \left ( 1+ix \right ) \right ) ^{-{\frac{3}{4}}}{\frac{1}{\sqrt [4]{-a \left ( -1+ix \right ) }}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a-I*a*x)^(13/4)/(a+I*a*x)^(3/4),x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{{\left (i \, a x + a\right )}^{\frac{3}{4}}{\left (-i \, a x + a\right )}^{\frac{13}{4}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((I*a*x + a)^(3/4)*(-I*a*x + a)^(13/4)),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.211563, size = 78, normalized size = 0.78 \[ \frac{2 \,{\left (i \, a x + a\right )}^{\frac{1}{4}}{\left (-i \, a x + a\right )}^{\frac{3}{4}}{\left (8 \, x^{2} + 20 i \, x - 17\right )}}{45 \, a^{5} x^{3} + 135 i \, a^{5} x^{2} - 135 \, a^{5} x - 45 i \, a^{5}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((I*a*x + a)^(3/4)*(-I*a*x + a)^(13/4)),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
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)**(13/4)/(a+I*a*x)**(3/4),x)
[Out]
_______________________________________________________________________________________
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)^(3/4)*(-I*a*x + a)^(13/4)),x, algorithm="giac")
[Out]