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

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

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

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

2 E (t ∣ \frac{1}{2}) + C

Solution steps

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

Use the nonelementary integral:

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

= 2 E (t ∣ \frac{1}{2})

Add a constant to the solution

= 2 E (t ∣ \frac{1}{2}) + C

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\int \frac{15}{x x ^{2} - 1} d x

sin (x) cos^{2} (x)

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