What is the integral from 1 to e of ln(21x) ?

The integral from 1 to e of ln(21x) is eln(21e)-e-ln(21)+1

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integral from 1 to e of ln(21x)

\int_{1}^{e} ln (21 x) d x

e ln (21 e) - e - ln (21) + 1

Decimal Notation

6.23134 \dots

Solution steps

\int_{1}^{e} ln (21 x) d x

Apply Integration By Parts

: [x ln (21 x) - \int 1 d x]_{1}^{e}

= [x ln (21 x) - \int 1 d x]_{1}^{e}

\int 1 d x = x

= [x ln (21 x) - x]_{1}^{e}

Compute the boundaries:

e ln (21 e) - e - ln (21) + 1

= e ln (21 e) - e - ln (21) + 1

x \to - 5 lim (x + 5)

\frac{\partial}{\partial z} (y^{2} z e^{z})

\frac{\partial}{\partial x} ((x^{2} + y^{2} + z^{2})^{- 0.5})

\int (sec (x) \cdot tan (x)) d x

y^{^{'}} + k y = 0

What is the integral from 1 to e of ln(21x) ?
The integral from 1 to e of ln(21x) is eln(21e)-e-ln(21)+1