What is the integral from 1 to 3 of 2ln(x) ?

The integral from 1 to 3 of 2ln(x) is 2(3ln(3)-2)

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integral from 1 to 3 of 2ln(x)

\int_{1}^{3} 2 ln (x) d x

2 (3 ln (3) - 2)

Decimal

2.59167 \dots

Solution steps

\int_{1}^{3} 2 ln (x) d x

Take the constant out:

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

= 2 \cdot \int_{1}^{3} ln (x) d x

Apply Integration By Parts

: [x ln (x) - \int 1 d x]_{1}^{3}

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

\int 1 d x = x

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

Compute the boundaries:

3 ln (3) - 2

= 2 (3 ln (3) - 2)

\int_{1}^{2} \frac{4}{2} d x

\int_{0}^{1} x x + 3 d x

\int_{0}^{4} \frac{3}{16} x d x

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

\int_{- 1}^{1} (x^{4} - x^{8}) d x

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