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

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

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

\int 1 d t = t

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

Compute the boundaries:

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

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

\int_{1}^{\frac{5}{4}} \frac{3}{4} x (2 - x)^{2} d x

\int_{0}^{1} x^{- 3} ln (x) d x

\int_{- 3}^{3} - x^{2} + 10 d x

\int_{b}^{\infty} \frac{1}{1 + x ^{2}} d x

\int_{0}^{3} (x + 2)^{2} d x

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