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

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

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integral of e^{-x+2}

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

- e^{- x + 2} + C

Solution steps

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

= - e^{- x + 2}

Add a constant to the solution

= - e^{- x + 2} + C

y = 4 (x + 1), y = 5 (x + 1), x = 5

f (x) = 9 sin (x) cos (x)

\int sin (x) cos (2 x) d x

cos (x^{3})

\int_{1}^{\infty} 5 e^{- 5 x} d x