What is the integral of t^4ln(t) ?

The integral of t^4ln(t) is 1/5 t^5ln(t)-(t^5)/(25)+C

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integral of t^4ln(t)

\int t^{4} ln (t) d t

\frac{1}{5} t^{5} ln (t) - \frac{t ^{5}}{25} + C

Solution steps

\int t^{4} ln (t) d t

Apply Integration By Parts

= \frac{1}{5} t^{5} ln (t) - \int \frac{t ^{4}}{5} d t

\int \frac{t ^{4}}{5} d t = \frac{t ^{5}}{25}

= \frac{1}{5} t^{5} ln (t) - \frac{t ^{5}}{25}

Add a constant to the solution

= \frac{1}{5} t^{5} ln (t) - \frac{t ^{5}}{25} + C

What is the integral of t^4ln(t) ?
The integral of t^4ln(t) is 1/5 t^5ln(t)-(t^5)/(25)+C