What is the integral from 1 to e of ln(5x^3) ?

The integral from 1 to e of ln(5x^3) is eln(5)-ln(5)+3

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integral from 1 to e of ln(5x^3)

\int_{1}^{e} ln (5 x^{3}) d x

e ln (5) - ln (5) + 3

Decimal Notation

5.76546 \dots

Solution steps

\int_{1}^{e} ln (5 x^{3}) d x

Apply Integration By Parts

: [x ln (5 x^{3}) - \int 3 d x]_{1}^{e}

= [x ln (5 x^{3}) - \int 3 d x]_{1}^{e}

\int 3 d x = 3 x

= [x ln (5 x^{3}) - 3 x]_{1}^{e}

Simplify

ln (5 x^{3}) : 3 ln (x) + ln (5)

= [x (ln (5) + 3 ln (x)) - 3 x]_{1}^{e}

Compute the boundaries:

e ln (5) - ln (5) + 3

= e ln (5) - ln (5) + 3

\int_{0}^{5} (7 x - x^{2}) - 2 x d x

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

\int_{1}^{2} t^{4} f (t^{5}) d t

y = 5 x^{3} - 5 x, (- 1, 0)

\frac{1000}{s + 1000}

What is the integral from 1 to e of ln(5x^3) ?
The integral from 1 to e of ln(5x^3) is eln(5)-ln(5)+3