What is the integral from 2 to 6 of ln(5x) ?

The integral from 2 to 6 of ln(5x) is 2ln(2700)-4

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integral from 2 to 6 of ln(5x)

\int_{2}^{6} ln (5 x) d x

2 ln (2700) - 4

Decimal

11.80201 \dots

Solution steps

\int_{2}^{6} ln (5 x) d x

Apply Integration By Parts

: [x ln (5 x) - \int 1 d x]_{2}^{6}

= [x ln (5 x) - \int 1 d x]_{2}^{6}

\int 1 d x = x

= [x ln (5 x) - x]_{2}^{6}

Compute the boundaries:

6 ln (30) - 4 - 2 ln (10)

= 6 ln (30) - 4 - 2 ln (10)

Simplify

= 2 ln (2700) - 4

\int 2 x ln (x^{2} + 5) d x

(4 e^{4 x})^{^{'}}

\frac{x ^{2} + 2 x - 3}{( x + 1 ) ^{2}}

f (x) = \frac{x}{1 + x ^{2}}, at x = 2

\frac{d}{d x} ((x + 2)^{a r c t a n (x)})

What is the integral from 2 to 6 of ln(5x) ?
The integral from 2 to 6 of ln(5x) is 2ln(2700)-4