What is the integral of x^x(ln(x)+1) ?

The integral of x^x(ln(x)+1) is x^x+C

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integral of x^x(ln(x)+1)

\int x^{x} (ln (x) + 1) d x

x^{x} + C

Solution steps

\int x^{x} (ln (x) + 1) d x

Apply u-substitution

: \int 1 d u

= \int 1 d u

Integral of a constant:

\int a d x = a x

= 1 \cdot u

Substitute back

u = x^{x}

= 1 \cdot x^{x}

Simplify

= x^{x}

Add a constant to the solution

= x^{x} + C

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