What is the integral of e^{bx} ?

The integral of e^{bx} is 1/b e^{bx}+C

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integral of e^{bx}

\int e^{b x} d x

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

Solution steps

\int e^{b x} d x

Apply u-substitution

: \int \frac{e ^{u}}{b} d u

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

u = b x

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

Add a constant to the solution

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

3 cos (t)

y^{^{''}} - 2 y^{^{'}} + y = 0, y (0) = - 1, y^{^{'}} (0) = - 2

c y^{- 3}

f (x) = ln (x + 5)

\frac{70}{x}