Optimal. Leaf size=16 \[ \frac {2 F\left (\left .\frac {1}{2} (a+b x)\right |2\right )}{b} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 16, 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 = {2641} \[ \frac {2 F\left (\left .\frac {1}{2} (a+b x)\right |2\right )}{b} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 2641
Rubi steps
\begin {align*} \int \frac {1}{\sqrt {\cos (a+b x)}} \, dx &=\frac {2 F\left (\left .\frac {1}{2} (a+b x)\right |2\right )}{b}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.03, size = 16, normalized size = 1.00 \[ \frac {2 F\left (\left .\frac {1}{2} (a+b x)\right |2\right )}{b} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [F] time = 0.39, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{\sqrt {\cos \left (b x + a\right )}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{\sqrt {\cos \left (b x + a\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [C] time = 0.13, size = 18, normalized size = 1.12 \[ \frac {2 \,\mathrm {am}^{-1}\left (\frac {b x}{2}+\frac {a}{2}| \sqrt {2}\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{\sqrt {\cos \left (b x + a\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.10, size = 15, normalized size = 0.94 \[ \frac {2\,\mathrm {F}\left (\frac {a}{2}+\frac {b\,x}{2}\middle |2\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{\sqrt {\cos {\left (a + b x \right )}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________