What is the integral of t^3ln(t) ?

The integral of t^3ln(t) is 1/4 t^4ln(t)-(t^4)/(16)+C

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integral of t^3ln(t)

\int t^{3} ln (t) d t

\frac{1}{4} t^{4} ln (t) - \frac{t ^{4}}{16} + C

Solution steps

\int t^{3} ln (t) d t

Apply Integration By Parts

: \frac{1}{4} t^{4} ln (t) - \int \frac{t ^{3}}{4} d t

= \frac{1}{4} t^{4} ln (t) - \int \frac{t ^{3}}{4} d t

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

= \frac{1}{4} t^{4} ln (t) - \frac{t ^{4}}{16}

Add a constant to the solution

= \frac{1}{4} t^{4} ln (t) - \frac{t ^{4}}{16} + C

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What is the integral of t^3ln(t) ?
The integral of t^3ln(t) is 1/4 t^4ln(t)-(t^4)/(16)+C