What is the integral from 0 to 1 of 6ln(x) ?

The integral from 0 to 1 of 6ln(x) is -6

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integral from 0 to 1 of 6ln(x)

\int_{0}^{1} 6 ln (x) d x

- 6

Solution steps

\int_{0}^{1} 6 ln (x) d x

Take the constant out:

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

= 6 \cdot \int_{0}^{1} ln (x) d x

Apply Integration By Parts

: [x ln (x) - \int 1 d x]_{0}^{1}

= 6 [x ln (x) - \int 1 d x]_{0}^{1}

\int 1 d x = x

= 6 [x ln (x) - x]_{0}^{1}

Compute the boundaries:

- 1

= 6 (- 1)

Simplify

= - 6

3 t^{2} - 5 e^{3 t}

x \to 2 a lim (\frac{x ^{2} - 2 a x + a ^{2}}{x ^{3} - a ^{3}})

\int_{2}^{4} 3 x d x

\frac{\partial}{\partial x} (arctan (2 x))

x \to - 1 lim (- 1 (x + 1))

What is the integral from 0 to 1 of 6ln(x) ?
The integral from 0 to 1 of 6ln(x) is -6