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))

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

\frac{d}{d x} (\frac{3 x - 1}{x + 1})

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

\frac{d}{d x} (8 (0.9)^{x - 2})

x y^{^{'}} = y^{2} - y, y (2) = 1

\int_{0}^{1} \frac{1}{( x ^{2} + 1 ) ^{3}} d x

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