What is the integral of cosh(2x) ?

The integral of cosh(2x) is 1/2 sinh(2x)+C

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integral of cosh(2x)

\int cosh (2 x) d x

\frac{1}{2} sinh (2 x) + C

Solution steps

\int cosh (2 x) d x

Apply u-substitution

: \int cosh (u) \frac{1}{2} d u

= \int cosh (u) \frac{1}{2} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int cosh (u) d u

Use the common integral:

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

= \frac{1}{2} sinh (u)

Substitute back

u = 2 x

= \frac{1}{2} sinh (2 x)

Add a constant to the solution

= \frac{1}{2} sinh (2 x) + C

x \to 0 lim (\frac{x}{x ^{2} - 2})

x \to 2 lim (\frac{x ^{2} + x}{x + 3})

x \to 1 lim (r (t))

\frac{x ^{2}}{ln ( 3 ^{x} )}

\int x ln (10 x) d x