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

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

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

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

sinh (x) + C

Solution steps

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

Rewrite using trig identities

= \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 3 cos (x) - 4 sin (x) d x

6 e^{6 x}

y = 5 - x^{2}, y = x^{2} - 3

\int \frac{1}{x 16 - x ^{2}} d x

f^{9}

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