What is the integral of e^{8t} ?

The integral of e^{8t} is 1/8 e^{8t}+C

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integral of e^{8t}

\int e^{8 t} d t

\frac{1}{8} e^{8 t} + C

Solution steps

\int e^{8 t} d t

Apply u-substitution

: \int e^{u} \frac{1}{8} d u

= \int e^{u} \frac{1}{8} d u

Take the constant out:

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

= \frac{1}{8} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{8} e^{u}

Substitute back

u = 8 t

= \frac{1}{8} e^{8 t}

Add a constant to the solution

= \frac{1}{8} e^{8 t} + C

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

t^{2} - 2 t

- \frac{7}{4 x}

\int \frac{x ^{4}}{8 - x ^{5}} d x

(x + y e^{\frac{y}{x}}) d x - x e^{\frac{y}{x}} d y = 0