What is the integral of 7xln(x) ?

The integral of 7xln(x) is 7(1/2 x^2ln(x)-(x^2)/4)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 7xln(x)

\int 7 x ln (x) d x

7 (\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}) + C

Solution steps

\int 7 x ln (x) d x

Take the constant out:

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

= 7 \cdot \int x ln (x) d x

Apply Integration By Parts

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

= 7 (\frac{1}{2} x^{2} ln (x) - \int \frac{x}{2} d x)

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

= 7 (\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4})

Add a constant to the solution

= 7 (\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}) + C

\int (2 + cos (x)) d x

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

\int 7 x e^{- 4 x^{2}} d x

\int csc (x) (sin (x) + cot (x)) d x

\int \frac{x - 1}{x ( x - 2 )} d x

What is the integral of 7xln(x) ?
The integral of 7xln(x) is 7(1/2 x^2ln(x)-(x^2)/4)+C