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

The integral from 3 to x^3 of ln(x) is 3x^3ln(x)-x^3-3ln(3)+3

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integral from 3 to x^3 of ln(x)

\int_{3}^{x^{3}} ln (x) d x

3 x^{3} ln (x) - x^{3} - 3 ln (3) + 3

Solution steps

\int_{3}^{x^{3}} ln (x) d x

Apply Integration By Parts

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

\int 1 d x = x

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

Compute the boundaries:

3 x^{3} ln (x) - x^{3} - 3 ln (3) + 3

= 3 x^{3} ln (x) - x^{3} - 3 ln (3) + 3

\int_{0}^{1} t e^{\frac{- t ^{2}}{2}} d t

\int_{1}^{t a n (5 x)} 1 - t d t

\int_{0}^{4} r d r

\int_{1}^{x} e^{t} d t

\int_{0}^{2} \frac{2 x}{2 + x ^{2}} d x

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