What is the integral from 0 to 2 of x^t ?

The integral from 0 to 2 of x^t is (x^2-1)/(ln(x))

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integral from 0 to 2 of x^t

\int_{0}^{2} x^{t} d t

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

Solution steps

\int_{0}^{2} x^{t} d t

\int a^{x} d x = \frac{a ^{x}}{ln a}

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

Compute the boundaries:

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

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

Simplify

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

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What is the integral from 0 to 2 of x^t ?
The integral from 0 to 2 of x^t is (x^2-1)/(ln(x))