What is the integral of e^x+e^{-x} ?

The integral of e^x+e^{-x} is 2sinh(x)+C

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integral of e^x+e^{-x}

\int e^{x} + e^{- x} d x

2 sinh (x) + C

Solution steps

\int e^{x} + e^{- x} d x

Rewrite using trig identities

= \int 2 cosh (x) d x

Take the constant out:

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

= 2 \cdot \int cosh (x) d x

Use the common integral:

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

= 2 sinh (x)

Add a constant to the solution

= 2 sinh (x) + C

\int (2 x y + 4 x^{3}) d x

x \to 0 + lim (\frac{ln ( x )}{x})

\int cot (43 x) d x

y = (3 x - 1)^{2}

n = 0 \sum \infty (1 - p)^{n}