What is the integral from 2 to 4 of x^{2x}(1+ln(x)) ?

The integral from 2 to 4 of x^{2x}(1+ln(x)) is 32760

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integral from 2 to 4 of x^{2x}(1+ln(x))

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

32760

Solution steps

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

Apply u-substitution

: \int_{16}^{65536} \frac{1}{2} d u

= \int_{16}^{65536} \frac{1}{2} d u

Integral of a constant:

\int a d x = a x

= [\frac{1}{2} u]_{16}^{65536}

Compute the boundaries:

32760

= 32760

\int_{2}^{4} x^{2} + 2 x d x

\int_{- 3}^{1} x^{2} d x

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

\int_{- 8}^{4} 32 - 4 x - x^{2} d x

\int_{- 1}^{1} x (x^{3} + cos^{3} (x)) d x

What is the integral from 2 to 4 of x^{2x}(1+ln(x)) ?
The integral from 2 to 4 of x^{2x}(1+ln(x)) is 32760