What is the integral of t^5ln(t) ?

The integral of t^5ln(t) is 1/6 t^6ln(t)-(t^6)/(36)+C

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integral of t^5ln(t)

\int t^{5} ln (t) d t

\frac{1}{6} t^{6} ln (t) - \frac{t ^{6}}{36} + C

Solution steps

\int t^{5} ln (t) d t

Apply Integration By Parts

= \frac{1}{6} t^{6} ln (t) - \int \frac{t ^{5}}{6} d t

\int \frac{t ^{5}}{6} d t = \frac{t ^{6}}{36}

= \frac{1}{6} t^{6} ln (t) - \frac{t ^{6}}{36}

Add a constant to the solution

= \frac{1}{6} t^{6} ln (t) - \frac{t ^{6}}{36} + C

d er i v a t i v e e^{(e^{(x)} - x)}

t an g e n t f (x) = 2 x^{2} + 3 x, (- 3, 9)

\frac{d}{d x} ((x^{3} - 1)^{4})

\frac{\partial}{\partial x} (11 - 4 x^{2} - y^{2})

\frac{\partial}{\partial x} (2 x^{3} y^{2} cos (6 x^{3} y))

What is the integral of t^5ln(t) ?
The integral of t^5ln(t) is 1/6 t^6ln(t)-(t^6)/(36)+C