What is the integral of 1/(((t+1)*t)) ?

The integral of 1/(((t+1)*t)) is -ln|t+1|+ln|t|+C

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integral of 1/(((t+1)*t))

integral

\frac{1}{( ( t + 1 ) \cdot t )}

- ln ∣ t + 1 ∣ + ln ∣ t ∣ + C

Solution steps

\int \frac{1}{( t + 1 ) t} d t

Take the partial fraction of

\frac{1}{( t + 1 ) t} : - \frac{1}{t + 1} + \frac{1}{t}

= \int - \frac{1}{t + 1} + \frac{1}{t} d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int \frac{1}{t + 1} d t + \int \frac{1}{t} d t

\int \frac{1}{t + 1} d t = ln ∣ t + 1 ∣

\int \frac{1}{t} d t = ln ∣ t ∣

= - ln ∣ t + 1 ∣ + ln ∣ t ∣

Add a constant to the solution

= - ln ∣ t + 1 ∣ + ln ∣ t ∣ + C

\frac{e ^{5} y + 5}{e ^{2} y - 5}

\frac{1}{x - x ^{2}}

\frac{x}{6}

\frac{arcsin ( x )}{x ^{2}}

\frac{2 y ^{2}}{x ^{3}}

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