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

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

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

\int 1 d t = t

= [t ln (t) - t]_{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_{0}^{4} \frac{1}{2} d x

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

\int_{0}^{L} sin^{2} (\frac{3 π x}{L}) d x

\int_{1}^{4} (x^{2} - x - 6) d x

\int_{6.3}^{6.6} 12 x^{2} - 6 x + \frac{4}{x} d x

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