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

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

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integral of e^{2x-3}

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

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

Solution steps

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

Apply u-substitution

= \int e^{u} \frac{1}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{2} e^{u}

Substitute back

u = 2 x - 3

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

Add a constant to the solution

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

\frac{d y}{d x} + \frac{y}{x} = \frac{3}{y}

\frac{d}{d x} (e^{x} (x - 2)^{2})

y = ln (a - 1)

\int \frac{x ^{2} + 6 x + 6}{x ^{3} + 9 x ^{2} + 18 x + 7} d x

\frac{d}{d x} (\frac{54}{( 3 x + 1 ) ^{4}})