What is the integral of 4ln(t) ?

The integral of 4ln(t) is 4(tln(t)-t)+C

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integral of 4ln(t)

\int 4 ln (t) d t

4 (t ln (t) - t) + C

Solution steps

\int 4 ln (t) d t

Take the constant out:

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

= 4 \cdot \int ln (t) d t

Apply Integration By Parts

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

= 4 (t ln (t) - \int 1 d t)

\int 1 d t = t

= 4 (t ln (t) - t)

Add a constant to the solution

= 4 (t ln (t) - t) + C

g (x) = sin (9 - 3 x)

f (x) = \frac{x}{9 x ^{2} - 1}

\frac{d}{d x} (ln (\frac{x + 3}{x - 3}))

x \to 0 + lim (\frac{x}{15 x ^{4} + 12 x})

x \to 2 lim (\frac{x ^{2} - 4}{x - 3})