What is the integral from 2 to 4 of 6xln(x) ?

The integral from 2 to 4 of 6xln(x) is 6(14ln(2)-3)

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integral from 2 to 4 of 6xln(x)

\int_{2}^{4} 6 x ln (x) d x

6 (14 ln (2) - 3)

Solution steps

\int_{2}^{4} 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_{2}^{4} x ln (x) d x

Apply Integration By Parts

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

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

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

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

Compute the boundaries:

14 ln (2) - 3

= 6 (14 ln (2) - 3)

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

\int_{0.2}^{1} 6 x (1 - x) d x

\int_{e}^{1} \frac{1}{x} d x

\int_{0}^{π} (cos^{2} (x)) d x

\int_{- 5}^{5} \frac{sin ( x )}{x} d x

What is the integral from 2 to 4 of 6xln(x) ?
The integral from 2 to 4 of 6xln(x) is 6(14ln(2)-3)