What is the integral from b to 1 of 4ln(x) ?

The integral from b to 1 of 4ln(x) is 4(-1-bln(b)+b)

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integral from b to 1 of 4ln(x)

\int_{b}^{1} 4 ln (x) d x

4 (- 1 - b ln (b) + b)

Solution steps

\int_{b}^{1} 4 ln (x) d x

Take the constant out:

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

= 4 \cdot \int_{b}^{1} ln (x) d x

Apply Integration By Parts

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

= 4 [x ln (x) - \int 1 d x]_{b}^{1}

\int 1 d x = x

= 4 [x ln (x) - x]_{b}^{1}

Compute the boundaries:

- 1 - b ln (b) + b

= 4 (- 1 - b ln (b) + b)

\frac{d y}{d x} + (\frac{4}{x}) y = 2 x + 1

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

(3 + x^{2})^{- 1}

n = 0 \sum \infty e^{(- 2 n)}

x \to 0 lim (2^{- \frac{1}{x ^{2}}})

What is the integral from b to 1 of 4ln(x) ?
The integral from b to 1 of 4ln(x) is 4(-1-bln(b)+b)