What is the integral from 1 to 2 of 3ln(4x) ?

The integral from 1 to 2 of 3ln(4x) is 3(4ln(2)-1)

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integral from 1 to 2 of 3ln(4x)

\int_{1}^{2} 3 ln (4 x) d x

3 (4 ln (2) - 1)

Decimal

5.31776 \dots

Solution steps

\int_{1}^{2} 3 ln (4 x) d x

Take the constant out:

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

= 3 \cdot \int_{1}^{2} ln (4 x) d x

Apply Integration By Parts

: [x ln (4 x) - \int 1 d x]_{1}^{2}

= 3 [x ln (4 x) - \int 1 d x]_{1}^{2}

\int 1 d x = x

= 3 [x ln (4 x) - x]_{1}^{2}

Compute the boundaries:

4 ln (2) - 1

= 3 (4 ln (2) - 1)

\int - 3 x^{- 2} d x

f (x) = (2 x^{3} + 1)^{2}, (- 1, 1)

x \to 0 lim (\frac{( e e ^{- a x} - e ^{- b x} )}{x})

f (x) = x^{3} - 3 x + 1

x = 36 - y^{2}, x = y^{2} - 36

What is the integral from 1 to 2 of 3ln(4x) ?
The integral from 1 to 2 of 3ln(4x) is 3(4ln(2)-1)