What is the integral of e^{4x+8} ?

The integral of e^{4x+8} is 1/4 e^{4x+8}+C

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integral of e^{4x+8}

\int e^{4 x + 8} d x

\frac{1}{4} e^{4 x + 8} + C

Solution steps

\int e^{4 x + 8} d x

Apply u-substitution

: \int e^{u} \frac{1}{4} d u

= \int e^{u} \frac{1}{4} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{4} e^{u}

Substitute back

u = 4 x + 8

= \frac{1}{4} e^{4 x + 8}

Add a constant to the solution

= \frac{1}{4} e^{4 x + 8} + C

f (x) = \frac{2 x + 1}{x - 1}

\frac{d}{d x} (\frac{\frac{d}{d x} ( ln ( x ) )}{x})

x^{2}, 8 + x

f (x) = - 3 e^{- 5 x}

\frac{d}{d x} (\frac{x + 4}{x - 3})