Question

integration of 1/x is​

Answer 1

Answer:

Hi mate.

Integration goes the other way: the integral (or antiderivative) of 1/x should be a function whose derivative is 1/x. As we just saw, this is ln(x). However, if x is negative then ln(x) is undefined.

You have

∫1xdx=ln|x|+C

(Note that the "constant" C might take different values for positive or negative x. It is really a locally constant function.)

In the same way,

∫f′(x)f(x)dx=ln|f(x)|+C

The last derivative is given by

ddx|f(x)|=sgn(f(x))f′(x)={f′(x)−f′(x) if f(x)>0 if f(x)<0 .

Hope it helps you mate.

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Answer 2

Answer:

Integration goes the other way: the integral (or antiderivative) of 1/x should be a function whose derivative is 1/x. As we just saw, this is ln(x). However, if x is negative then ln(x) is undefined! The solution is quite simple: the antiderivative of 1/x is ln(|x|).