What is the integral from 0 to 1 of 4ln(x) ?

The integral from 0 to 1 of 4ln(x) is -4

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integral from 0 to 1 of 4ln(x)

\int_{0}^{1} 4 ln (x) d x

- 4

Solution steps

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

Apply Integration By Parts

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

= 4 [x ln (x) - \int 1 d x]_{0}^{1}

\int 1 d x = x

= 4 [x ln (x) - x]_{0}^{1}

Compute the boundaries:

- 1

= 4 (- 1)

Simplify

= - 4

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

\frac{d}{d x} (\frac{5}{4 x}) - \frac{7}{4}

\int \frac{( arctan ( x ) ) ^{3}}{1 + x ^{2}} d x

\frac{\partial}{\partial x} (\frac{x}{x ^{2} + ( y - 1 ) ^{2}})

\int \frac{1}{12 x} d x

What is the integral from 0 to 1 of 4ln(x) ?
The integral from 0 to 1 of 4ln(x) is -4