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

The integral of (ln(t))/3 is 1/3 (tln(t)-t)+C

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integral of (ln(t))/3

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

\frac{1}{3} (t ln (t) - t) + C

Solution steps

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

Take the constant out:

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

= \frac{1}{3} \cdot \int ln (t) d t

Apply Integration By Parts

: t ln (t) - \int 1 d t

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

\int 1 d t = t

= \frac{1}{3} (t ln (t) - t)

Add a constant to the solution

= \frac{1}{3} (t ln (t) - t) + C

\int \frac{x}{( x + 3 ) ^{5}} d x

\int (x + 1) sin (2 x - 3) d x

y^{^{''}} - 20 y^{^{'}} + 181 y = 0

\int (x^{2} - 5)^{2} d x

\int \frac{x}{x} d x

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