What is the integral of-e^{2-x} ?

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

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integral of-e^{2-x}

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

e^{2 - x} + C

Solution steps

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

Take the constant out:

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

= - \int e^{2 - x} d x

Apply u-substitution

: \int - e^{u} d u

= - \int - e^{u} d u

Take the constant out:

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

= - (- \int e^{u} d u)

Use the common integral:

\int e^{u} d u = e^{u}

= - (- e^{u})

Substitute back

u = 2 - x

= - (- e^{2 - x})

Simplify

= e^{2 - x}

Add a constant to the solution

= e^{2 - x} + C

\frac{\partial}{\partial x} (x sin (x + 2 y))

n = 1 \sum \infty \frac{n !}{10 3 ^{n}}

f (x) = x + \frac{3}{x}, at x = 2

E

f (x) = e^{- x} - e^{- x} x