What is the integral from 1 to e of ln(15x) ?

The integral from 1 to e of ln(15x) is eln(15e)-e-ln(15)+1

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integral from 1 to e of ln(15x)

\int_{1}^{e} ln (15 x) d x

e ln (15 e) - e - ln (15) + 1

Decimal Notation

5.65319 \dots

Solution steps

\int_{1}^{e} ln (15 x) d x

Apply Integration By Parts

: [x ln (15 x) - \int 1 d x]_{1}^{e}

= [x ln (15 x) - \int 1 d x]_{1}^{e}

\int 1 d x = x

= [x ln (15 x) - x]_{1}^{e}

Compute the boundaries:

e ln (15 e) - e - ln (15) + 1

= e ln (15 e) - e - ln (15) + 1

\frac{d}{d x} (- \frac{20}{( 2 + x ) ^{2}})

e^{x} - \frac{8}{x}

x^{4} + 1

\int \frac{1}{x ^{\frac{1}{3}}} d x

\frac{d}{d x} (ln (\frac{5}{x}))

What is the integral from 1 to e of ln(15x) ?
The integral from 1 to e of ln(15x) is eln(15e)-e-ln(15)+1