Optimal. Leaf size=19 \[ -\frac {2 F\left (\left .\frac {\pi }{4}-\frac {b x}{2}\right |2\right )}{b} \]
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Rubi [A] time = 0.01, antiderivative size = 19, normalized size of antiderivative = 1.00, 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.
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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*}
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Mathematica [A] time = 0.02, 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.
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fricas [F] time = 0.42, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{\sqrt {\sin \left (b x\right )}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{\sqrt {\sin \left (b x\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 57, normalized size = 3.00 \[ \frac {\sqrt {\sin \left (b x \right )+1}\, \sqrt {-2 \sin \left (b x \right )+2}\, \sqrt {-\sin \left (b x \right )}\, \EllipticF \left (\sqrt {\sin \left (b x \right )+1}, \frac {\sqrt {2}}{2}\right )}{\cos \left (b x \right ) \sqrt {\sin \left (b x \right )}\, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{\sqrt {\sin \left (b x\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.39, size = 15, normalized size = 0.79 \[ -\frac {2\,\mathrm {F}\left (\frac {\pi }{4}-\frac {b\,x}{2}\middle |2\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{\sqrt {\sin {\left (b x \right )}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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