Question

Integral 3t+ 1 / (t + 1)^2​

Answer 1

`3ln|t+1|+(2)/(t+1) +C`

Step-by-step explanation:

We'll be using u-substitution for this problem.

Let

`u=t+1\\du=dt`

Substitute

`\int\limits {(3u-2)/(u^2)} \, du`

Split the fraction

`\int\limits {(3u)/(u^2) } \, du -\int\limits {(2)/(u^2) } \, du`

Move the constants out

`3\int\limits {(u)/(u^2)du -2\int\limits {u^(-2)} \, du`

Simplify

`3\int\limits {(1)/(u)du -2\int\limits {u^(-2)} \, du`

Integrate

`3ln|u|+(2)/(u) +C`

Substitute

`3ln|t+1|+(2)/(t+1) +C`