What is the integral from 0 to 1 of 5ln(4x) ?

The integral from 0 to 1 of 5ln(4x) is 5(2ln(2)-1)

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integral from 0 to 1 of 5ln(4x)

\int_{0}^{1} 5 ln (4 x) d x

5 (2 ln (2) - 1)

Decimal Notation

1.93147 \dots

Solution steps

\int_{0}^{1} 5 ln (4 x) d x

Take the constant out:

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

= 5 \cdot \int_{0}^{1} ln (4 x) d x

Apply Integration By Parts

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

= 5 [x ln (4 x) - \int 1 d x]_{0}^{1}

\int 1 d x = x

= 5 [x ln (4 x) - x]_{0}^{1}

Compute the boundaries:

2 ln (2) - 1

= 5 (2 ln (2) - 1)

x + 3, \frac{1}{2} x + 3

\frac{d x}{d t} = x e^{t} - 3 e^{t} + x - 3

\int_{0}^{60} 60 e^{- 0.02 x} d x

(0, - 9), (4, - 10)

What is the integral from 0 to 1 of 5ln(4x) ?
The integral from 0 to 1 of 5ln(4x) is 5(2ln(2)-1)