What is the integral of-tln(t) ?

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

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integral of-tln(t)

\int - t ln (t) d t

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

Solution steps

\int - t ln (t) d t

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int t ln (t) d t

Apply Integration By Parts

: \frac{1}{2} t^{2} ln (t) - \int \frac{t}{2} d t

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

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

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

Simplify

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

Add a constant to the solution

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

x^{2}, at x = 0

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

\int [\frac{4}{16 x ^{2} + 1}] d x

f (x) = x^{2} - 5 x + 5, (6, 11)

\frac{\partial}{\partial s} (s + t)

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