What is the integral from b to 1 of 5ln(x) ?

The integral from b to 1 of 5ln(x) is 5(-1-bln(b)+b)

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integral from b to 1 of 5ln(x)

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

5 (- 1 - b ln (b) + b)

Solution steps

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

Take the constant out:

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

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

Apply Integration By Parts

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

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

\int 1 d x = x

= 5 [x ln (x) - x]_{b}^{1}

Compute the boundaries:

- 1 - b ln (b) + b

= 5 (- 1 - b ln (b) + b)

y^{^{''}} - \frac{y}{4} = 0

\frac{d}{d x} (\frac{4}{16 x ^{2} + 1})

\frac{\partial}{\partial x} (e^{x y})

y = (\frac{3 x ^{2}}{2 x + 4})^{3}

\frac{5}{s ( s ^{2} + 5 ^{2} )}

What is the integral from b to 1 of 5ln(x) ?
The integral from b to 1 of 5ln(x) is 5(-1-bln(b)+b)