What is the integral of e^{3x-2} ?

The integral of e^{3x-2} is 1/3 e^{3x-2}+C

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integral of e^{3x-2}

\int e^{3 x - 2} d x

\frac{1}{3} e^{3 x - 2} + C

Solution steps

\int e^{3 x - 2} 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 - 2

= \frac{1}{3} e^{3 x - 2}

Add a constant to the solution

= \frac{1}{3} e^{3 x - 2} + C

\frac{d y}{d x} - 9 y^{2} e^{- 1 x} = 0, y (0) = 5

y = x^{4}, at x = 0

cos (5 t)

\int x (\frac{1}{4} e^{- \frac{x}{4}}) d x

2 x^{2}, x^{2} + 5