What is the integral of (e^5)/(e^x) ?

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

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integral of (e^5)/(e^x)

\int \frac{e ^{5}}{e ^{x}} d x

- e^{5 - x} + C

Solution steps

\int \frac{e ^{5}}{e ^{x}} d x

Take the constant out:

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

= e^{5} \cdot \int \frac{1}{e ^{x}} d x

Apply u-substitution

: \int \frac{1}{u ^{2}} d u

= e^{5} \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= e^{5} (- \frac{1}{u})

Substitute back

u = e^{x}

= e^{5} (- \frac{1}{e ^{x}})

Simplify

e^{5} (- \frac{1}{e ^{x}}) : - e^{5 - x}

= - e^{5 - x}

Add a constant to the solution

= - e^{5 - x} + C

\int \frac{( cos ( x ) + sin ( x ) )}{sin ( 2 x )} d x

\frac{d}{d x} (C x e^{x})

\int_{0}^{1} 6

\frac{\partial}{\partial x} (x z - 5 x^{2} y^{3} z^{4})

\frac{\partial}{\partial x} (\frac{3 x - 2 y}{x ^{2} + 3 y})