What is the integral from 0 to 1 of 3ln(x) ?

The integral from 0 to 1 of 3ln(x) is -3

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integral from 0 to 1 of 3ln(x)

\int_{0}^{1} 3 ln (x) d x

- 3

Solution steps

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

Apply Integration By Parts

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

= 3 [x ln (x) - \int 1 d x]_{0}^{1}

\int 1 d x = x

= 3 [x ln (x) - x]_{0}^{1}

Compute the boundaries:

- 1

= 3 (- 1)

Simplify

= - 3

\int cos (x) sin (n x) d x

\frac{d}{d x} ((cos (3 x)) \cdot 3)

f (x) = - x

ln (\frac{x}{2}), 2

\int_{0}^{2} \frac{1}{( x ^{2} + 4 ) ^{2}} d x

What is the integral from 0 to 1 of 3ln(x) ?
The integral from 0 to 1 of 3ln(x) is -3