What is the integral from 0 to 1 of 4ln(3x) ?

The integral from 0 to 1 of 4ln(3x) is 4(ln(3)-1)

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integral from 0 to 1 of 4ln(3x)

\int_{0}^{1} 4 ln (3 x) d x

4 (ln (3) - 1)

Decimal Notation

0.39444 \dots

Solution steps

\int_{0}^{1} 4 ln (3 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 (3 x) d x

Apply Integration By Parts

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

= 4 [x ln (3 x) - \int 1 d x]_{0}^{1}

\int 1 d x = x

= 4 [x ln (3 x) - x]_{0}^{1}

Compute the boundaries:

ln (3) - 1

= 4 (ln (3) - 1)

\int \frac{1}{x ^{2} + 2 x + 37} d x

\int t e^{5 t} d t

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

\int (9 x^{2} - 5 x + 3) d x

x \to 2 lim ((x - 2)^{x - 2})

What is the integral from 0 to 1 of 4ln(3x) ?
The integral from 0 to 1 of 4ln(3x) is 4(ln(3)-1)