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

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

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

\int 1 d x = x

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

Compute the boundaries:

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

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

\int_{2}^{8} x^{2} - 2 x - 15 d x

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

\int_{1}^{2} 2 x e^{- x^{2}} d x

\int_{1}^{4} e^{3 x} d x

\int_{0}^{s i n (x)} e^{- t^{2}} d t

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