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

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

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integral of e^{8x+3}

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

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

Solution steps

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

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 x + 3

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

Add a constant to the solution

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

\int_{0}^{\frac{π}{2}} 17 sin^{2} (2 x) d x

x^{4} + 2 x, x = 1

y = \frac{4 x ^{2} + 8 x + 8}{x}

\frac{\partial}{\partial y} (ln (x - 4 y))

x \to 1 lim (2 x^{3} + x - 1)