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Question Number 106743 by mohammad17 last updated on 06/Aug/20

$$\int \sqrt{secy}dy$$

Answered by Sarah85 last updated on 07/Aug/20

$$\int \sqrt{\sec y}dy=\int \frac{dy}{\sqrt{\cos y}}=\int \frac{dy}{\sqrt{1-{2\sin }^2\frac{y}{2}}}$$$$\mathrm{let}t=\frac{y}{2}$$$$2\int \frac{dt}{\sqrt{1-{2\sin }^{2}t}}=2F(t\mid 2)=$$$$=2F(\frac{y}{2}\mid 2)+C$$

Commented by Her_Majesty last updated on 07/Aug/20

$$youthink{he}^{\prime }ssatisfiedwiththisanswer?$$

Commented by Sarah85 last updated on 07/Aug/20

$$\mathrm{not}\mathrm{sure},\mathrm{anyway}\mathrm{this}IS\mathrm{the}\mathrm{answer}$$

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