What is the integral from 1 to e of ln(16x) ?

The integral from 1 to e of ln(16x) is eln(16e)-e-4ln(2)+1

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integral from 1 to e of ln(16x)

\int_{1}^{e} ln (16 x) d x

e ln (16 e) - e - 4 ln (2) + 1

Decimal

5.76408 \dots

Solution steps

\int_{1}^{e} ln (16 x) d x

Apply Integration By Parts

: [x ln (16 x) - \int 1 d x]_{1}^{e}

= [x ln (16 x) - \int 1 d x]_{1}^{e}

\int 1 d x = x

= [x ln (16 x) - x]_{1}^{e}

Compute the boundaries:

e ln (16 e) - e - 4 ln (2) + 1

= e ln (16 e) - e - 4 ln (2) + 1

x \to 1 lim (\frac{4 - 3 x}{1 - x})

\int_{1}^{1000} \frac{17}{x ^{3}} d x

\frac{d}{d t} (\frac{sec ^{2} ( t )}{cos ( t ) ( sec ( t ) )})

\int_{0}^{1} \frac{59}{4 y - 1} d y

\frac{d}{d x} (3 cos (x) + 3 x sin (x))

What is the integral from 1 to e of ln(16x) ?
The integral from 1 to e of ln(16x) is eln(16e)-e-4ln(2)+1