What is the integral of 5ln(2x) ?

The integral of 5ln(2x) is 5(xln(2x)-x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 5ln(2x)

\int 5 ln (2 x) d x

5 (x ln (2 x) - x) + C

Solution steps

\int 5 ln (2 x) d x

Take the constant out:

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

= 5 \cdot \int ln (2 x) d x

Apply Integration By Parts

: x ln (2 x) - \int 1 d x

= 5 (x ln (2 x) - \int 1 d x)

\int 1 d x = x

= 5 (x ln (2 x) - x)

Add a constant to the solution

= 5 (x ln (2 x) - x) + C

\int \frac{e ^{2 x}}{3 e ^{2 x} + 5} d x

\int \frac{4 x ^{3} + 2 x ^{2} - x + 3}{x} d x

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

\int e^{20 x} 6 sin (2 x) d x

\int x \cdot sin (x) d x