What is the integral of ln(4x^2) ?

The integral of ln(4x^2) is 2xln(2x)-2x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ln(4x^2)

\int ln (4 x^{2}) d x

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

Solution steps

\int ln (4 x^{2}) d x

Apply Integration By Parts

: x ln (4 x^{2}) - \int 2 d x

= x ln (4 x^{2}) - \int 2 d x

\int 2 d x = 2 x

= x ln (4 x^{2}) - 2 x

Simplify

ln (4 x^{2}) : 2 ln (2 x)

= 2 x ln (2 x) - 2 x

Add a constant to the solution

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

x \to \frac{3 π}{2} + lim (tan (x))

\frac{5 s}{( s - 2 ) ^{2}}

\frac{x}{1 - x ^{3}}

\int \frac{4 e ^{3 x}}{1 + e ^{2 x}} d x

\int_{0}^{4} x 2 x + 1 d x