What is the integral of e^{5-x} ?

The integral of e^{5-x} is -e^{5-x}+C

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integral of e^{5-x}

\int e^{5 - x} d x

- e^{5 - x} + C

Solution steps

\int e^{5 - 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 = 5 - x

= - e^{5 - x}

Add a constant to the solution

= - e^{5 - x} + C

\int 10 x 5 x^{2} - 1 d x

\int_{0}^{1} (2 x - 1)^{6} d x

\int \frac{1}{( 5 x - 2 ) ^{\frac{3}{2}}} d x

x \to 2 lim (sin (x - 2) + 1)

(y^{2} - x y) d x + x^{2} d y = 0