Optimal. Leaf size=21 \[ \frac {2 E\left (\left .\frac {1}{2} \left (a+b x-\frac {\pi }{2}\right )\right |2\right )}{b} \]
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Rubi [A] time = 0.01, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {2639} \[ \frac {2 E\left (\left .\frac {1}{2} \left (a+b x-\frac {\pi }{2}\right )\right |2\right )}{b} \]
Antiderivative was successfully verified.
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Rule 2639
Rubi steps
\begin {align*} \int \sqrt {\sin (a+b x)} \, dx &=\frac {2 E\left (\left .\frac {1}{2} \left (a-\frac {\pi }{2}+b x\right )\right |2\right )}{b}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 24, normalized size = 1.14 \[ -\frac {2 E\left (\left .\frac {1}{2} \left (-a-b x+\frac {\pi }{2}\right )\right |2\right )}{b} \]
Antiderivative was successfully verified.
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fricas [F] time = 0.46, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\sqrt {\sin \left (b x + a\right )}, x\right ) \]
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 \[ \int \sqrt {\sin \left (b x + a\right )}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 91, normalized size = 4.33 \[ -\frac {\sqrt {\sin \left (b x +a \right )+1}\, \sqrt {-2 \sin \left (b x +a \right )+2}\, \sqrt {-\sin \left (b x +a \right )}\, \left (2 \EllipticE \left (\sqrt {\sin \left (b x +a \right )+1}, \frac {\sqrt {2}}{2}\right )-\EllipticF \left (\sqrt {\sin \left (b x +a \right )+1}, \frac {\sqrt {2}}{2}\right )\right )}{\cos \left (b x +a \right ) \sqrt {\sin \left (b x +a \right )}\, b} \]
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 \[ \int \sqrt {\sin \left (b x + a\right )}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.37, size = 18, normalized size = 0.86 \[ \frac {2\,\mathrm {E}\left (\frac {a}{2}-\frac {\pi }{4}+\frac {b\,x}{2}\middle |2\right )}{b} \]
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 \[ \int \sqrt {\sin {\left (a + b x \right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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