What is the integral of t^8ln(t) ?

The integral of t^8ln(t) is 1/9 t^9ln(t)-(t^9)/(81)+C

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integral of t^8ln(t)

\int t^{8} ln (t) d t

\frac{1}{9} t^{9} ln (t) - \frac{t ^{9}}{81} + C

Solution steps

\int t^{8} ln (t) d t

Apply Integration By Parts

: \frac{1}{9} t^{9} ln (t) - \int \frac{t ^{8}}{9} d t

= \frac{1}{9} t^{9} ln (t) - \int \frac{t ^{8}}{9} d t

\int \frac{t ^{8}}{9} d t = \frac{t ^{9}}{81}

= \frac{1}{9} t^{9} ln (t) - \frac{t ^{9}}{81}

Add a constant to the solution

= \frac{1}{9} t^{9} ln (t) - \frac{t ^{9}}{81} + C

f (x) = \frac{1}{x + 6}

\frac{d}{d x} ((7 x)^{l n (7 x)})

\int_{0}^{2 π} sin (t) d t

\frac{d}{d x} (9 lo g_{2} (x))

n \to \infty lim (e^{- n})

What is the integral of t^8ln(t) ?
The integral of t^8ln(t) is 1/9 t^9ln(t)-(t^9)/(81)+C