What is the integral from 1/2 to 5 of 10xln(2x) ?

The integral from 1/2 to 5 of 10xln(2x) is 10(-99/16+25/2 ln(10))

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 5 of 10xln(2x)

\int_{\frac{1}{2}}^{5} 10 x ln (2 x) d x

10 (- \frac{99}{16} + \frac{25}{2} ln (10))

Decimal Notation

225.94813 \dots

Solution steps

\int_{\frac{1}{2}}^{5} 10 x ln (2 x) d x

Take the constant out:

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

= 10 \cdot \int_{\frac{1}{2}}^{5} 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}}^{5}

= 10 [\frac{1}{2} x^{2} ln (2 x) - \int \frac{x}{2} d x]_{\frac{1}{2}}^{5}

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

= 10 [\frac{1}{2} x^{2} ln (2 x) - \frac{x ^{2}}{4}]_{\frac{1}{2}}^{5}

Compute the boundaries:

- \frac{99}{16} + \frac{25}{2} ln (10)

= 10 (- \frac{99}{16} + \frac{25}{2} ln (10))

f (x) = 5 x^{- 15}

f (t) = 1 - cos (t)

\frac{x d y}{d x} + y = e^{x}

\frac{d}{d x} (tan (x) + x^{4})

\int arcsin (x) d x

What is the integral from 1/2 to 5 of 10xln(2x) ?
The integral from 1/2 to 5 of 10xln(2x) is 10(-99/16+25/2 ln(10))