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

The integral from 1 to 5 of ln(4x) is ln(800000)-4

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integral from 1 to 5 of ln(4x)

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

ln (800000) - 4

Decimal

9.59236 \dots

Solution steps

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

Apply Integration By Parts

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

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

\int 1 d x = x

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

Compute the boundaries:

5 ln (20) - 4 - 2 ln (2)

= 5 ln (20) - 4 - 2 ln (2)

Simplify

= ln (800000) - 4

\int_{1}^{3} (8 - 2 x) d x

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

\int_{0}^{2 π} 4 d t

\int_{- 2}^{3} (4 x - 5) d x

\int_{0}^{3} \frac{1}{3} x^{3} d x

What is the integral from 1 to 5 of ln(4x) ?
The integral from 1 to 5 of ln(4x) is ln(800000)-4