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How do you find the indefinite integral of #f(x) = 1/(x+1)#?

Answer 1

Cameron Alexander

you have: #int(1/(x+1))dx=ln|x+1|+c#

Try to derive back your result and you'll find #f(x)#;

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Answer 2

Scarlett Allison

To find the indefinite integral of ( f(x) = \frac{1}{x+1} ), you can use the technique of integration by substitution. Let ( u = x + 1 ). Then, ( du/dx = 1 ) implies ( dx = du ). Substituting these into the integral:

[ \int \frac{1}{x+1} dx = \int \frac{1}{u} du = \ln|u| + C = \ln|x + 1| + C ]

where ( C ) is the constant of integration.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.