What is the integral from 1/2 to 7 of 6xln(2x) ?

The integral from 1/2 to 7 of 6xln(2x) is 6(-195/16+49/2 ln(14))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 1/2 to 7 of 6xln(2x)

\int_{\frac{1}{2}}^{7} 6 x ln (2 x) d x

6 (- \frac{195}{16} + \frac{49}{2} ln (14))

Decimal

314.81642 \dots

Solution steps

\int_{\frac{1}{2}}^{7} 6 x ln (2 x) d x

Take the constant out:

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

= 6 \cdot \int_{\frac{1}{2}}^{7} x ln (2 x) d x

Apply Integration By Parts

: [\frac{1}{2} x^{2} ln (2 x) - \int \frac{x}{2} d x]_{\frac{1}{2}}^{7}

= 6 [\frac{1}{2} x^{2} ln (2 x) - \int \frac{x}{2} d x]_{\frac{1}{2}}^{7}

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

= 6 [\frac{1}{2} x^{2} ln (2 x) - \frac{x ^{2}}{4}]_{\frac{1}{2}}^{7}

Compute the boundaries:

- \frac{195}{16} + \frac{49}{2} ln (14)

= 6 (- \frac{195}{16} + \frac{49}{2} ln (14))

\int_{- \infty}^{- 1} e^{- 2 t} d t

\frac{d}{d y} (ln (x + y))

f (x) = 2^{40}

sin (x), cos (x), [- π, π]

\int \frac{20 s + 20}{( s ^{2} + 1 ) ( s - 1 ) ^{3}} d s

What is the integral from 1/2 to 7 of 6xln(2x) ?
The integral from 1/2 to 7 of 6xln(2x) is 6(-195/16+49/2 ln(14))