What is the integral of sqrt(cos^2(x)+1) ?

The integral of sqrt(cos^2(x)+1) is sqrt(2)\E(x\vert 1/2)+C

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integral of sqrt(cos^2(x)+1)

\int cos^{2} (x) + 1 d x

2 E (x ∣ \frac{1}{2}) + C

Solution steps

\int cos^{2} (x) + 1 d x

Use the nonelementary integral:

\int cos^{2} (x) + 1 d x = 2 E (x ∣ \frac{1}{2})

= 2 E (x ∣ \frac{1}{2})

Add a constant to the solution

= 2 E (x ∣ \frac{1}{2}) + C

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What is the integral of sqrt(cos^2(x)+1) ?
The integral of sqrt(cos^2(x)+1) is sqrt(2)\E(x\vert 1/2)+C