Question

Integral 3t+ 1 / (t + 1)^2​

Answer 1

Answer:

$3ln|t+1|+\frac{2}{t+1} +C$

Explanation:

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

Let

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

Substitute

$\int\limits {\frac{3u-2}{u^2}} \, du$

Split the fraction

$\int\limits {\frac{3u}{u^2} } \, du -\int\limits {\frac{2}{u^2} } \, du$

Move the constants out

$3\int\limits {\frac{u}{u^2}du -2\int\limits {u^{-2}} \, du$

Simplify

$3\int\limits {\frac{1}{u}du -2\int\limits {u^{-2}} \, du$

Integrate

$3ln|u|+\frac{2}{u} +C$

Substitute

$3ln|t+1|+\frac{2}{t+1} +C$