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

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

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

integral

1 + cos^{2} (x)

2 E (x ∣ \frac{1}{2}) + C

Solution steps

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

Use the nonelementary integral:

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

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