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

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

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

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

E (x ∣ - 1) + C

Solution steps

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

Simplify

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

Use the nonelementary integral:

\int 1 + c \cdot sin^{2} (x) d x = E (x ∣ - c)

= E (x ∣ - 1)

Add a constant to the solution

= E (x ∣ - 1) + C

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