What is the integral of-1/2 e^{2x} ?

The integral of-1/2 e^{2x} is -1/4 e^{2x}+C

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integral of-1/2 e^{2x}

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

- \frac{1}{4} e^{2 x} + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

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

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

Use the common integral:

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

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

Substitute back

u = 2 x

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

Simplify

- \frac{1}{2} \cdot \frac{1}{2} e^{2 x} : - \frac{1}{4} e^{2 x}

= - \frac{1}{4} e^{2 x}

Add a constant to the solution

= - \frac{1}{4} e^{2 x} + C

\frac{\partial}{\partial y} (e^{3 x - y})

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

\int \frac{1}{3} x d x

y = x^{2} sin (2 x)

\frac{d}{d x} (\frac{a}{( x ^{2} + a ^{2} ) ^{2}})

What is the integral of-1/2 e^{2x} ?
The integral of-1/2 e^{2x} is -1/4 e^{2x}+C