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

The integral from 1 to 3 of 2(1+ln(x))x^{2x} is 728

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integral from 1 to 3 of 2(1+ln(x))x^{2x}

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

728

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int_{1}^{3} (1 + ln (x)) x^{2 x} d x

Apply u-substitution

: \int_{1}^{729} \frac{1}{2} d u

= 2 \cdot \int_{1}^{729} \frac{1}{2} d u

Integral of a constant:

\int a d x = a x

= 2 [\frac{1}{2} u]_{1}^{729}

Compute the boundaries:

364

= 2 \cdot 364

Simplify

= 728

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What is the integral from 1 to 3 of 2(1+ln(x))x^{2x} ?
The integral from 1 to 3 of 2(1+ln(x))x^{2x} is 728