What is the integral of e^{ln(2x)} ?

The integral of e^{ln(2x)} is x^2+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{ln(2x)}

\int e^{l n (2 x)} d x

x^{2} + C

Solution steps

\int e^{l n (2 x)} d x

Apply log rule:

a^{l o g_{a} (b)} = b

= \int 2 x d x

Take the constant out:

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

= 2 \cdot \int x d x

Apply the Power Rule

: \frac{x ^{2}}{2}

= 2 \cdot \frac{x ^{2}}{2}

Simplify

2 \cdot \frac{x ^{2}}{2} : x^{2}

= x^{2}

Add a constant to the solution

= x^{2} + C

x \to 0 lim (\frac{5 x cot ( 3 x )}{2 sec ( x )})

f (t) = 2 t sin (π t)

\int \frac{4 x ^{2} + 21 x + 54}{x ^{2} + 6 x + 13} d x

x \to 8 lim (6 x^{2} - 9 x + 1)

(\frac{3}{2})^{x}