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

The integral from b to 1 of 3ln(x) is 3(-1-bln(b)+b)

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integral from b to 1 of 3ln(x)

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

3 (- 1 - b ln (b) + b)

Solution steps

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

Take the constant out:

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

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

Apply Integration By Parts

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

\int 1 d x = x

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

Compute the boundaries:

- 1 - b ln (b) + b

= 3 (- 1 - b ln (b) + b)

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