What is the integral from 1 to 2 of (1+ln(x))x^x ?

The integral from 1 to 2 of (1+ln(x))x^x is 3

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integral from 1 to 2 of (1+ln(x))x^x

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

3

Solution steps

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

Apply u-substitution

: \int_{1}^{4} 1 d u

= \int_{1}^{4} 1 d u

Integral of a constant:

\int a d x = a x

= [1 \cdot u]_{1}^{4}

Simplify

= [u]_{1}^{4}

Compute the boundaries:

3

= 3

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\int_{e}^{e^{2}} \frac{1}{x ln ^{3} ( x )} d x

\int_{1}^{2} \frac{1}{9} x^{2} d x

\int_{0}^{7} (2 x - 7) d x

What is the integral from 1 to 2 of (1+ln(x))x^x ?
The integral from 1 to 2 of (1+ln(x))x^x is 3