Optimal. Leaf size=33 \[ -\frac{2 i (a+i a x)^{3/4}}{3 a^2 (a-i a x)^{3/4}} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0032194, 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, Rules used = {37} \[ -\frac{2 i (a+i a x)^{3/4}}{3 a^2 (a-i a x)^{3/4}} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 37
Rubi steps
\begin{align*} \int \frac{1}{(a-i a x)^{7/4} \sqrt [4]{a+i a x}} \, dx &=-\frac{2 i (a+i a x)^{3/4}}{3 a^2 (a-i a x)^{3/4}}\\ \end{align*}
Mathematica [A] time = 0.013589, size = 33, normalized size = 1. \[ -\frac{2 i (a+i a x)^{3/4}}{3 a^2 (a-i a x)^{3/4}} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.03, size = 31, normalized size = 0.9 \begin{align*}{\frac{2\,x-2\,i}{3\,a} \left ( -a \left ( -1+ix \right ) \right ) ^{-{\frac{3}{4}}}{\frac{1}{\sqrt [4]{a \left ( 1+ix \right ) }}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (i \, a x + a\right )}^{\frac{1}{4}}{\left (-i \, a x + a\right )}^{\frac{7}{4}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.5323, size = 78, normalized size = 2.36 \begin{align*} \frac{2 \,{\left (i \, a x + a\right )}^{\frac{3}{4}}{\left (-i \, a x + a\right )}^{\frac{1}{4}}}{3 \,{\left (a^{3} x + i \, a^{3}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{\sqrt [4]{a \left (i x + 1\right )} \left (- a \left (i x - 1\right )\right )^{\frac{7}{4}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: TypeError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]