What is the integral of t^3ln(t^2) ?

The integral of t^3ln(t^2) is 1/2 t^4ln(t)-(t^4)/8+C

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integral of t^3ln(t^2)

\int t^{3} ln (t^{2}) d t

\frac{1}{2} t^{4} ln (t) - \frac{t ^{4}}{8} + C

Solution steps

\int t^{3} ln (t^{2}) d t

Apply Integration By Parts

= \frac{1}{4} t^{4} ln (t^{2}) - \int \frac{t ^{3}}{2} d t

\int \frac{t ^{3}}{2} d t = \frac{t ^{4}}{8}

= \frac{1}{4} t^{4} ln (t^{2}) - \frac{t ^{4}}{8}

\frac{1}{4} t^{4} ln (t^{2}) = \frac{1}{2} t^{4} ln (t)

= \frac{1}{2} t^{4} ln (t) - \frac{t ^{4}}{8}

Add a constant to the solution

= \frac{1}{2} t^{4} ln (t) - \frac{t ^{4}}{8} + C

What is the integral of t^3ln(t^2) ?
The integral of t^3ln(t^2) is 1/2 t^4ln(t)-(t^4)/8+C