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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of-e^{2x}

\int - e^{2 x} d x

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

Solution steps

\int - e^{2 x} d x

Take the constant out:

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

= - \int e^{2 x} 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

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

Add a constant to the solution

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

h \to 0 lim (\frac{6 ^{h} - 1}{h})

\frac{s ^{2}}{s ^{2} + 20 s + 100}

\int e^{2 θ} sin (3 θ) d θ

x \to - 1 lim (x^{2} - 2)

\int \frac{1}{1000 - x} d x