What is the integral of 1/3 e^{2-x} ?

The integral of 1/3 e^{2-x} is -1/3 e^{2-x}+C

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integral of 1/3 e^{2-x}

\int \frac{1}{3} e^{2 - x} d x

- \frac{1}{3} e^{2 - x} + C

Solution steps

\int \frac{1}{3} e^{2 - x} d x

Take the constant out:

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

= \frac{1}{3} \cdot \int e^{2 - x} d x

Apply u-substitution

: \int - e^{u} d u

= \frac{1}{3} \cdot \int - e^{u} d u

Take the constant out:

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

= \frac{1}{3} (- \int e^{u} d u)

Use the common integral:

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

= \frac{1}{3} (- e^{u})

Substitute back

u = 2 - x

= \frac{1}{3} (- e^{2 - x})

Simplify

= - \frac{1}{3} e^{2 - x}

Add a constant to the solution

= - \frac{1}{3} e^{2 - x} + C

\frac{d}{d x} (x 36 - x^{2})

\frac{d}{d x} ((2 x + 3) (5 x^{2} - 4 x))

\int_{0}^{b} e^{\frac{x}{2}} d x

\int \frac{x ^{3}}{3 x} d x

x \to 2 lim (\frac{f ( x )}{g ( x )})

What is the integral of 1/3 e^{2-x} ?
The integral of 1/3 e^{2-x} is -1/3 e^{2-x}+C