What is the integral from 1 to 2 of xln(sqrt(x)) ?

The integral from 1 to 2 of xln(sqrt(x)) is ln(2)-3/8

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 1 to 2 of xln(sqrt(x))

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

ln (2) - \frac{3}{8}

Decimal Notation

0.31814 \dots

Solution steps

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

Apply Integration By Parts

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

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

\int \frac{x}{4} d x = \frac{x ^{2}}{8}

= [\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{8}]_{1}^{2}

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

= [\frac{1}{4} x^{2} ln (x) - \frac{x ^{2}}{8}]_{1}^{2}

Compute the boundaries:

ln (2) - \frac{3}{8}

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

\int_{7}^{9} (x^{2} + 2 x - 6) d x

\int_{0}^{1} (2 a + 1)^{4} d a

\int_{0}^{1} f (t) d t

\int_{1}^{6} \frac{3}{x} d x

\int_{π}^{2 π} θ d θ

What is the integral from 1 to 2 of xln(sqrt(x)) ?
The integral from 1 to 2 of xln(sqrt(x)) is ln(2)-3/8