What is the integral of e^{3x-8} ?

The integral of e^{3x-8} is 1/3 e^{3x-8}+C

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integral of e^{3x-8}

\int e^{3 x - 8} d x

\frac{1}{3} e^{3 x - 8} + C

Solution steps

\int e^{3 x - 8} d x

Apply u-substitution

: \int e^{u} \frac{1}{3} d u

= \int e^{u} \frac{1}{3} d u

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

u = 3 x - 8

= \frac{1}{3} e^{3 x - 8}

Add a constant to the solution

= \frac{1}{3} e^{3 x - 8} + C

\frac{d}{d x} (e^{c o s (4 x)})

(6.3) (7.8)

33 x^{3}

\int \frac{a + b x ^{7}}{8 a x + b x ^{8}} d x

f (x) = 4 e^{x} + x, at x = 0