What is the integral from b to 1 of 8ln(x) ?

The integral from b to 1 of 8ln(x) is 8(-1-bln(b)+b)

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integral from b to 1 of 8ln(x)

\int_{b}^{1} 8 ln (x) d x

8 (- 1 - b ln (b) + b)

Solution steps

\int_{b}^{1} 8 ln (x) d x

Take the constant out:

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

= 8 \cdot \int_{b}^{1} ln (x) d x

Apply Integration By Parts

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

= 8 [x ln (x) - \int 1 d x]_{b}^{1}

\int 1 d x = x

= 8 [x ln (x) - x]_{b}^{1}

Compute the boundaries:

- 1 - b ln (b) + b

= 8 (- 1 - b ln (b) + b)

\int \frac{y}{( y ^{2} + 1 ) ^{\frac{1}{2}}} d y

\frac{\partial}{\partial y} (\frac{x}{z - 2 y})

\frac{\partial}{\partial x} (e^{8 x} cos (- 9 y))

e^{- 6 x}

\frac{d}{d x} (2 sin (x) cos (x))

What is the integral from b to 1 of 8ln(x) ?
The integral from b to 1 of 8ln(x) is 8(-1-bln(b)+b)