What is the integral of e^{4x} 4/3 ?

The integral of e^{4x} 4/3 is 1/3 e^{4x}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{4x} 4/3

\int e^{4 x} \frac{4}{3} d x

\frac{1}{3} e^{4 x} + C

Solution steps

\int e^{4 x} \frac{4}{3} d x

Take the constant out:

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

= \frac{4}{3} \cdot \int e^{4 x} d x

Apply u-substitution

: \int e^{u} \frac{1}{4} d u

= \frac{4}{3} \cdot \int e^{u} \frac{1}{4} d u

Take the constant out:

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

= \frac{4}{3} \cdot \frac{1}{4} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{4}{3} \cdot \frac{1}{4} e^{u}

Substitute back

u = 4 x

= \frac{4}{3} \cdot \frac{1}{4} e^{4 x}

Simplify

\frac{4}{3} \cdot \frac{1}{4} e^{4 x} : \frac{1}{3} e^{4 x}

= \frac{1}{3} e^{4 x}

Add a constant to the solution

= \frac{1}{3} e^{4 x} + C

\int y (y^{2} + 5)^{8} d y

\int x^{2} (1 + x)^{2} d x

\int 324 - x^{2} d x

\int \frac{x ^{2} + 2 x - 3}{x ^{3} - 2 x ^{2} + x - 2} d x

\int - \frac{e ^{x}}{( e ^{x} + 1 ) ^{3}} d x