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

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

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integral of e^{2x-2}

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

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

Solution steps

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

Apply u-substitution

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

= \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 - 2

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

Add a constant to the solution

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

\frac{d}{d x} (\frac{1}{2 x ^{2} - 3})

\int \frac{( e ^{x^{2}} - 1 )}{x} d x

\int_{0}^{1} \frac{1}{( x - 1 ) ^{2}} d x

\frac{1 + x}{1 - x}

\int_{0}^{3} π (2 x)^{2} d x