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Sagot :

Hi !

[tex]∫ \frac{t}{t + 1}dt[/tex]

We need to prove that it is equal to

[tex]∫ \frac{u - 1}{u}du[/tex]

As per given options, Substitute u by t+1

[tex] = > ∫ \frac{u - 1}{t + 1} du[/tex]

Then given t = u-1

[tex] = > ∫ \frac{t}{t + 1} du[/tex]

Then substitue the third given value also

[tex] = > ∫ \frac{t}{t + 1} dt[/tex]

Therefore, it's proved

~Hope it helps

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