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

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

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

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

2 E (x ∣ \frac{1}{2}) + C

Solution steps

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

Simplify

= \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

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