What is the integral from 4 to 8 of t^3ln(5t) ?

The integral from 4 to 8 of t^3ln(5t) is 1024ln(40)-240-64ln(20)

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integral from 4 to 8 of t^3ln(5t)

\int_{4}^{8} t^{3} ln (5 t) d t

1024 ln (40) - 240 - 64 ln (20)

Decimal Notation

3345.68569 \dots

Solution steps

\int_{4}^{8} t^{3} ln (5 t) d t

Apply Integration By Parts

: [\frac{1}{4} t^{4} ln (5 t) - \int \frac{t ^{3}}{4} d t]_{4}^{8}

= [\frac{1}{4} t^{4} ln (5 t) - \int \frac{t ^{3}}{4} d t]_{4}^{8}

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

= [\frac{1}{4} t^{4} ln (5 t) - \frac{t ^{4}}{16}]_{4}^{8}

Compute the boundaries:

1024 ln (40) - 240 - 64 ln (20)

= 1024 ln (40) - 240 - 64 ln (20)

x y^{^{'}} + 2 y = 2 cos (x)

\frac{x ^{2} - 9 x + 1}{x ^{2} + 5}

5 sin^{2} (t)

\frac{d}{d x} (4 x sin (x^{2}))

\frac{d}{d x} (\frac{2 - x}{1 - y})

What is the integral from 4 to 8 of t^3ln(5t) ?
The integral from 4 to 8 of t^3ln(5t) is 1024ln(40)-240-64ln(20)