Answered

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integral 3t+ 1 / (t + 1)^2​

Sagot :

Answer:

[tex]3ln|t+1|+\frac{2}{t+1} +C[/tex]

Explanation:

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

Let

[tex]u=t+1\\du=dt[/tex]

Substitute

[tex]\int\limits {\frac{3u-2}{u^2}} \, du[/tex]

Split the fraction

[tex]\int\limits {\frac{3u}{u^2} } \, du -\int\limits {\frac{2}{u^2} } \, du[/tex]

Move the constants out

[tex]3\int\limits {\frac{u}{u^2}du -2\int\limits {u^{-2}} \, du[/tex]

Simplify

[tex]3\int\limits {\frac{1}{u}du -2\int\limits {u^{-2}} \, du[/tex]

Integrate

[tex]3ln|u|+\frac{2}{u} +C[/tex]

Substitute

[tex]3ln|t+1|+\frac{2}{t+1} +C[/tex]

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