What is the integral of (ln(t))/((t+1)^2) ?

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

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integral of (ln(t))/((t+1)^2)

integral

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

\frac{x ^{2}}{( x ^{2} - 2 x + 2 ) ^{2}}

(u^{2}) (1 + u^{2})^{0.5}

6^{x}

\frac{( ln ( x ) ) ^{3}}{x}

e^{2 x - x^{2}}

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