What is the integral of 3xln(x^8) ?

The integral of 3xln(x^8) is 3(4x^2ln(x)-2x^2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 3xln(x^8)

\int 3 x ln (x^{8}) d x

3 (4 x^{2} ln (x) - 2 x^{2}) + C

Solution steps

\int 3 x ln (x^{8}) d x

Take the constant out:

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

= 3 \cdot \int x ln (x^{8}) d x

Apply Integration By Parts

: \frac{1}{2} x^{2} ln (x^{8}) - \int 4 x d x

= 3 (\frac{1}{2} x^{2} ln (x^{8}) - \int 4 x d x)

\int 4 x d x = 2 x^{2}

= 3 (\frac{1}{2} x^{2} ln (x^{8}) - 2 x^{2})

\frac{1}{2} x^{2} ln (x^{8}) = 4 x^{2} ln (x)

= 3 (4 x^{2} ln (x) - 2 x^{2})

Add a constant to the solution

= 3 (4 x^{2} ln (x) - 2 x^{2}) + C

(x - 7) (2 x - 9)

\frac{\partial}{\partial x} (x^{2} cos (x) y)

\int e^{- θ} cos (2 θ) d θ

\int (2 x - 9) e^{2 x} d x

\frac{d}{d x} (- \frac{3 y}{3 x + 2 y})

What is the integral of 3xln(x^8) ?
The integral of 3xln(x^8) is 3(4x^2ln(x)-2x^2)+C