Optimal. Leaf size=19 \[ -\frac{2 F\left (\left .\frac{\pi }{4}-\frac{b x}{2}\right |2\right )}{b} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.008046, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125, Rules used = {2641} \[ -\frac{2 F\left (\left .\frac{\pi }{4}-\frac{b x}{2}\right |2\right )}{b} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2641
Rubi steps
\begin{align*} \int \frac{1}{\sqrt{\sin (b x)}} \, dx &=-\frac{2 F\left (\left .\frac{\pi }{4}-\frac{b x}{2}\right |2\right )}{b}\\ \end{align*}
Mathematica [A] time = 0.024718, size = 21, normalized size = 1.11 \[ -\frac{2 F\left (\left .\frac{1}{2} \left (\frac{\pi }{2}-b x\right )\right |2\right )}{b} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.034, size = 57, normalized size = 3. \begin{align*}{\frac{1}{b\cos \left ( bx \right ) }\sqrt{\sin \left ( bx \right ) +1}\sqrt{-2\,\sin \left ( bx \right ) +2}\sqrt{-\sin \left ( bx \right ) }{\it EllipticF} \left ( \sqrt{\sin \left ( bx \right ) +1},{\frac{\sqrt{2}}{2}} \right ){\frac{1}{\sqrt{\sin \left ( bx \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}{\sqrt{\sin \left (b x\right )}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [F] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{1}{\sqrt{\sin \left (b x\right )}}, x\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{\sin{\left (b x \right )}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{\sqrt{\sin \left (b x\right )}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]