What is the integral from 2 to x^3 of ln(x) ?

The integral from 2 to x^3 of ln(x) is 3x^3ln(x)-x^3-2ln(2)+2

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integral from 2 to x^3 of ln(x)

\int_{2}^{x^{3}} ln (x) d x

3 x^{3} ln (x) - x^{3} - 2 ln (2) + 2

Solution steps

\int_{2}^{x^{3}} ln (x) d x

Apply Integration By Parts

: [x ln (x) - \int 1 d x]_{2}^{x^{3}}

= [x ln (x) - \int 1 d x]_{2}^{x^{3}}

\int 1 d x = x

= [x ln (x) - x]_{2}^{x^{3}}

Compute the boundaries:

3 x^{3} ln (x) - x^{3} - 2 ln (2) + 2

= 3 x^{3} ln (x) - x^{3} - 2 ln (2) + 2

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\int_{0}^{\frac{1}{3}} arcsin (3 x) d x

What is the integral from 2 to x^3 of ln(x) ?
The integral from 2 to x^3 of ln(x) is 3x^3ln(x)-x^3-2ln(2)+2