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

The integral of sqrt(1+(sinh(x))^2) is sinh(x)+C

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

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

sinh (x) + C

Solution steps

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

Simplify

1 + (sinh (x))^{2} : cosh^{2} (x)

= \int cosh^{2} (x) d x

cosh^{2} (x) = (cosh (x)),

assuming

cosh (x) \geq 0

= \int cosh (x) d x

Use the common integral:

\int cosh (x) d x = sinh (x)

= sinh (x)

Add a constant to the solution

= sinh (x) + C

\int 2 e^{- 2 y} d y

\frac{d}{d x} (e^{g (x) (x^{3}) - 2})

y^{^{''}} + 4 y^{^{'}} + 6 y = 0, y (0) = - 4, y^{^{'}} (0) = - 1

\frac{x + 1}{x ^{2} - 4 x}

\int csc^{2} (x) + 7 d x

What is the integral of sqrt(1+(sinh(x))^2) ?
The integral of sqrt(1+(sinh(x))^2) is sinh(x)+C