What is the integral of e^{(-x+2)/3} ?

The integral of e^{(-x+2)/3} is -3e^{(-x+2)/3}+C

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integral of e^{(-x+2)/3}

\int e^{\frac{- x + 2}{3}} d x

- 3 e^{\frac{- x + 2}{3}} + C

Solution steps

\int e^{\frac{- x + 2}{3}} d x

Apply u-substitution

: \int - e^{\frac{u}{3}} d u

= \int - e^{\frac{u}{3}} d u

Take the constant out:

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

= - \int e^{\frac{u}{3}} d u

Apply u-substitution

: \int e^{v} \cdot 3 d v

= - \int e^{v} \cdot 3 d v

Take the constant out:

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

= - 3 \cdot \int e^{v} d v

Use the common integral:

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

= - 3 e^{v}

Substitute back

= - 3 e^{\frac{- x + 2}{3}}

Add a constant to the solution

= - 3 e^{\frac{- x + 2}{3}} + C

y^{^{''}} - 16 y = \frac{16 x}{e ^{4 x}}

\int_{0}^{\infty} 2 x e^{- x} d x

\int e^{- \frac{1}{2} x^{2}} d x

y^{^{''}} + 2 y + y = 2 e^{- t}

\frac{x}{x - 2}

What is the integral of e^{(-x+2)/3} ?
The integral of e^{(-x+2)/3} is -3e^{(-x+2)/3}+C