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

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

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integral of 1/3 e^{x+3}

\int \frac{1}{3} e^{x + 3} d x

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

Solution steps

\int \frac{1}{3} e^{x + 3} 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^{x + 3} d x

e^{x + 3} = e^{3} e^{x}

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

Take the constant out:

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

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

Use the common integral:

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

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

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{3} e^{x} = e^{3 + x}

= \frac{1}{3} e^{3 + x}

Add a constant to the solution

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

5 x + 1, at x = 3

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

6 sec (x), at x = \frac{π}{6}

\frac{d}{d x} (\frac{x + 1}{x ^{2} + x + 1})

x \to - 2 lim (f (x) x)

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