What is the integral from 3 to 4 of xln(x) ?

The integral from 3 to 4 of xln(x) is 16ln(2)-7/4-9/2 ln(3)

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integral from 3 to 4 of xln(x)

\int_{3}^{4} x ln (x) d x

16 ln (2) - \frac{7}{4} - \frac{9}{2} ln (3)

Decimal

4.39659 \dots

Solution steps

\int_{3}^{4} x ln (x) d x

Apply Integration By Parts

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

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

= [\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}]_{3}^{4}

Compute the boundaries:

16 ln (2) - \frac{7}{4} - \frac{9}{2} ln (3)

= 16 ln (2) - \frac{7}{4} - \frac{9}{2} ln (3)

\int_{5}^{10} \frac{6}{25} x d x

\int_{3}^{4} \frac{3}{x} d x

\int_{0}^{3} 4^{2 x} d x

\int_{- 1}^{1} \frac{2 x}{x ^{2} + 1} d x

\int_{- 1}^{1} ∣ x ∣ cos (nπ x) d x

What is the integral from 3 to 4 of xln(x) ?
The integral from 3 to 4 of xln(x) is 16ln(2)-7/4-9/2 ln(3)