Optimal. Leaf size=60 \[ \frac{1}{3} \text{Unintegrable}\left (\frac{x}{\sqrt{\cos (a+b x)}},x\right )+\frac{4 \cos ^{\frac{3}{2}}(a+b x)}{9 b^2}+\frac{2 x \sin (a+b x) \sqrt{\cos (a+b x)}}{3 b} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0377989, 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 = {} \[ \int x \cos ^{\frac{3}{2}}(a+b x) \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int x \cos ^{\frac{3}{2}}(a+b x) \, dx &=\frac{4 \cos ^{\frac{3}{2}}(a+b x)}{9 b^2}+\frac{2 x \sqrt{\cos (a+b x)} \sin (a+b x)}{3 b}+\frac{1}{3} \int \frac{x}{\sqrt{\cos (a+b x)}} \, dx\\ \end{align*}
Mathematica [A] time = 2.02598, size = 0, normalized size = 0. \[ \int x \cos ^{\frac{3}{2}}(a+b x) \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.122, size = 0, normalized size = 0. \begin{align*} \int x \left ( \cos \left ( bx+a \right ) \right ) ^{{\frac{3}{2}}}\, 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 x \cos \left (b x + a\right )^{\frac{3}{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: UnboundLocalError} \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 x \cos \left (b x + a\right )^{\frac{3}{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]