compute-the-indefinite-integral-sech-x2-dxdisplaystyle-int-operatornamesechleftd

Question

Compute the indefinite integral ∫sech⁡ ⁣(x2)dx{\displaystyle\int\operatorname{sech}\!\left(\dfrac{x}{2}\right)dx}.

Accepted Answer

2sin⁡−1(tanh⁡(x2))+C\displaystyle2\$$sin^{-1}$$\bigl(	anh(	frac{x}{2})\bigr)+C

Answer

12sin⁡−1(tanh⁡(x2))+C\displaystyle\dfrac{1}{2}\$$sin^{-1}$$\bigl(	anh(	frac{x}{2})\bigr)+C

Answer

ln⁡∣tanh⁡(x4)∣+C\displaystyle\ln\bigl|	anh(	frac{x}{4})\bigr|+C

Answer

sinh−1(tanh(x2))+C	extrm{sinh}^{-1} \left ( 	extrm{tanh}\left ( \frac{x}{2} ight ) ight )+C

Compute the indefinite integral ∫sech(x2)dx{\(\displaystyle\]\int\[\operatorname{sech}\)\!\(\left\)(\(\dfrac{x}{2}\]\right\))dx}.