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

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

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

2 x ln (x) - 2 x + C

Solution steps

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

Apply Integration By Parts

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

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

\int 2 d x = 2 x

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

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

= 2 x ln (x) - 2 x

Add a constant to the solution

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

\int 2 x (x^{2} + 2)^{- 3} d x

i = 1 \sum \infty 8 (\frac{5}{6})^{i - 1}

(cos (x))^{2} π

y^{^{'}} = \frac{x - 3}{y + 5}

\frac{d}{d x} (- 2 e^{4 x})