What is the integral from-1 to 1 of x(e^x+e^{-x}) ?

The integral from-1 to 1 of x(e^x+e^{-x}) is 0

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integral from-1 to 1 of x(e^x+e^{-x})

\int_{- 1}^{1} x (e^{x} + e^{- x}) d x

0

Solution steps

\int_{- 1}^{1} x (e^{x} + e^{- x}) d x

If f(x) is an odd function and continuous at:

[- a, a]

then

\int_{- a}^{a} f (x) d x = 0

Parity of

x (e^{x} + e^{- x}) :

Odd

= 0

What is the integral from-1 to 1 of x(e^x+e^{-x}) ?
The integral from-1 to 1 of x(e^x+e^{-x}) is 0