What is the integral from 0 to 1 of x^0ln(x) ?

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

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integral from 0 to 1 of x^0ln(x)

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

- 1

Solution steps

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

Simplify

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

Apply Integration By Parts

: [x ln (x) - \int 1 d x]_{0}^{1}

= [x ln (x) - \int 1 d x]_{0}^{1}

\int 1 d x = x

= [x ln (x) - x]_{0}^{1}

Compute the boundaries:

- 1

= - 1

\int_{- 1}^{4} \frac{1}{4 - x} d x

\int_{0}^{\frac{π}{2}} \frac{1}{2 + cos ( x )} d x

\int_{1}^{- 1} (9 r + 8)^{2} d r

\int_{1}^{4} \frac{1}{( x + 1 ) ^{2}} d x

\int_{0}^{4} ln (x) d x

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