What is the integral from 1 to 5 of 6xln(x) ?

The integral from 1 to 5 of 6xln(x) is 6(-6+25/2 ln(5))

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integral from 1 to 5 of 6xln(x)

\int_{1}^{5} 6 x ln (x) d x

6 (- 6 + \frac{25}{2} ln (5))

Decimal Notation

84.70784 \dots

Solution steps

\int_{1}^{5} 6 x ln (x) d x

Take the constant out:

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

= 6 \cdot \int_{1}^{5} x ln (x) d x

Apply Integration By Parts

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

= 6 [\frac{1}{2} x^{2} ln (x) - \int \frac{x}{2} d x]_{1}^{5}

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

= 6 [\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}]_{1}^{5}

Compute the boundaries:

- 6 + \frac{25}{2} ln (5)

= 6 (- 6 + \frac{25}{2} ln (5))

\int cos (x + n x) d x

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\int \frac{5 + u}{u} d u

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

What is the integral from 1 to 5 of 6xln(x) ?
The integral from 1 to 5 of 6xln(x) is 6(-6+25/2 ln(5))