What is the integral from 2 to 6 of t^3ln(4t) ?

The integral from 2 to 6 of t^3ln(4t) is 324ln(24)-80-12ln(2)

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integral from 2 to 6 of t^3ln(4t)

\int_{2}^{6} t^{3} ln (4 t) d t

324 ln (24) - 80 - 12 ln (2)

Solution steps

\int_{2}^{6} t^{3} ln (4 t) d t

Apply Integration By Parts

: [\frac{1}{4} t^{4} ln (4 t) - \int \frac{t ^{3}}{4} d t]_{2}^{6}

= [\frac{1}{4} t^{4} ln (4 t) - \int \frac{t ^{3}}{4} d t]_{2}^{6}

\int \frac{t ^{3}}{4} d t = \frac{t ^{4}}{16}

= [\frac{1}{4} t^{4} ln (4 t) - \frac{t ^{4}}{16}]_{2}^{6}

Compute the boundaries:

324 ln (24) - 80 - 12 ln (2)

= 324 ln (24) - 80 - 12 ln (2)

y^{^{'}} = 5 y sin (4 x), y (\frac{π}{8}) = 3

n = 1 \sum \infty \frac{1}{π ^{n}}

x \to 0 lim (x (\frac{1}{2 x}))

y^{^{''}} + 2 y^{^{'}} - 63 y = 0

(x - 4)^{n}, 4

What is the integral from 2 to 6 of t^3ln(4t) ?
The integral from 2 to 6 of t^3ln(4t) is 324ln(24)-80-12ln(2)