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

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

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

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

2 x^{2} ln (x) - x^{2} - \frac{x ln ( x )}{2} + x

Solution steps

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

Apply Integration By Parts

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

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

\int 1 d x = x

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

Compute the boundaries:

2 x^{2} ln (x) - x^{2} - \frac{1}{2} x ln (x) + x

= 2 x^{2} ln (x) - x^{2} - \frac{1}{2} x ln (x) + x

Simplify

= 2 x^{2} ln (x) - x^{2} - \frac{x ln ( x )}{2} + x

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