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What is the Integral of #(x+1)/x dx#?

Answer 1

Emilia Aguilar

Not many people realize this, but the key to doing this is to separate it using the additive properties of integrals.

#int (x+1)/xdx#

#= int cancel(x/x)dx + int 1/xdx#

#= int dx + int 1/xdx#

#= color(blue)(x + ln|x| + C)#

where you'll have to remember that the integral of #1/u((du)/(dx))# is #ln|u|#. You'll see it a lot more later.

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Answer 2

Emilia Aguilar

The integral of (x+1)/x dx is ln|x| + x + 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.