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

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

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

\int 1 d t = t

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

Compute the boundaries:

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

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

Simplify

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

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