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

The integral from 1 to e of ln(5x) is eln(5e)-e-ln(5)+1

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integral from 1 to e of ln(5x)

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

e ln (5 e) - e - ln (5) + 1

Decimal Notation

3.76546 \dots

Solution steps

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

Apply Integration By Parts

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

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

\int 1 d x = x

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

Compute the boundaries:

e ln (5 e) - e - ln (5) + 1

= e ln (5 e) - e - ln (5) + 1

x + 1

\frac{d}{d x} (∣ x ∣^{a})

\int \frac{1}{x ^{2} 36 x ^{2} - 1} d x

x^{s i n (x)}

f (x) = \frac{3 x}{( x + 1 ) ^{2}}, at x = 0

What is the integral from 1 to e of ln(5x) ?
The integral from 1 to e of ln(5x) is eln(5e)-e-ln(5)+1