What is the integral of 1/3 e^t ?

The integral of 1/3 e^t is 1/3 e^t+C

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integral of 1/3 e^t

\int \frac{1}{3} e^{t} d t

\frac{1}{3} e^{t} + C

Solution steps

\int \frac{1}{3} e^{t} d t

Take the constant out:

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

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

Use the common integral:

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

= \frac{1}{3} e^{t}

Add a constant to the solution

= \frac{1}{3} e^{t} + C

f (x) = ln (\frac{5 x + 3}{5 x - 3})

x^{2} + x \frac{d y}{d x} = y

\frac{\partial}{\partial y} (- 3 y)

y^{^{'}} + \frac{t}{t ^{2} - 16} y = \frac{e ^{t}}{t - 9}

n = 0 \sum \infty cos (nπ)