What is the integral from 4 to 7 of x^4ln(2x) ?

The integral from 4 to 7 of x^4ln(2x) is 16807/5 ln(14)-16807/25-(3072/5 ln(2)-1024/25)

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integral from 4 to 7 of x^4ln(2x)

\int_{4}^{7} x^{4} ln (2 x) d x

\frac{16807}{5} ln (14) - \frac{16807}{25} - (\frac{3072}{5} ln (2) - \frac{1024}{25})

Decimal Notation

7813.73768 \dots

Solution steps

\int_{4}^{7} x^{4} ln (2 x) d x

Compute the indefinite integral:

\int x^{4} ln (2 x) d x = \frac{1}{5} x^{5} ln (2 x) - \frac{x ^{5}}{25} + C

Compute the boundaries:

\int_{4}^{7} x^{4} ln (2 x) d x = \frac{16807}{5} ln (14) - \frac{16807}{25} - (\frac{3072}{5} ln (2) - \frac{1024}{25})

= \frac{16807}{5} ln (14) - \frac{16807}{25} - (\frac{3072}{5} ln (2) - \frac{1024}{25})

x \to 8 lim (\frac{x ^{8}}{x - 8})

\int - \frac{10}{t + 7} d t

\frac{d}{d x} (3 x^{2} + 8 x)

\frac{d y}{d x} = 6 x^{2} - x^{2} y

x y - 3 y^{2} = 6, (9, 2)

What is the integral from 4 to 7 of x^4ln(2x) ?
The integral from 4 to 7 of x^4ln(2x) is 16807/5 ln(14)-16807/25-(3072/5 ln(2)-1024/25)