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

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

= 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)

\int 5 x \frac{3}{2} d x

\frac{d y}{d x} - (sin (x)) y = 2 sin (x)

\frac{d}{d x} (\frac{e ^{- x}}{x})

\int_{- 1}^{1} e^{y} - (y^{2} - 9) d y

(14 - 6 y + e - 3 x) d x - 2 d y = 0

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)