Optimal. Leaf size=27 \[ \text{Unintegrable}\left (\frac{(a+b \sec (c+d x))^{3/2}}{\sqrt [3]{\sec (c+d x)}},x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0579205, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{(a+b \sec (c+d x))^{3/2}}{\sqrt [3]{\sec (c+d x)}} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \frac{(a+b \sec (c+d x))^{3/2}}{\sqrt [3]{\sec (c+d x)}} \, dx &=\int \frac{(a+b \sec (c+d x))^{3/2}}{\sqrt [3]{\sec (c+d x)}} \, dx\\ \end{align*}
Mathematica [A] time = 37.1165, size = 0, normalized size = 0. \[ \int \frac{(a+b \sec (c+d x))^{3/2}}{\sqrt [3]{\sec (c+d x)}} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.192, size = 0, normalized size = 0. \begin{align*} \int{ \left ( a+b\sec \left ( dx+c \right ) \right ) ^{{\frac{3}{2}}}{\frac{1}{\sqrt [3]{\sec \left ( dx+c \right ) }}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\left (b \sec \left (d x + c\right ) + a\right )}^{\frac{3}{2}}}{\sec \left (d x + c\right )^{\frac{1}{3}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{{\left (b \sec \left (d x + c\right ) + a\right )}^{\frac{3}{2}}}{\sec \left (d x + c\right )^{\frac{1}{3}}}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\left (b \sec \left (d x + c\right ) + a\right )}^{\frac{3}{2}}}{\sec \left (d x + c\right )^{\frac{1}{3}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]