1.

Integration of x to the power of - 1 dx

Answer»

\implies \sf \displaystyle \int \sf{<klux>X</klux>}^{ - <klux>1</klux>} dx

We know that :-

\implies \sf \boxed{ \displaystyle \sf{a}^{ - 1} = \frac{1}{a} }

\implies \sf \displaystyle \int \sf{x}^{ - 1} dx = \sf \displaystyle \int \sf \dfrac{1}{x} dx

\implies\sf \displaystyle \int \sf \dfrac{1}{x} dx = log(x) + c

Where c is constant.

Answer :

\sf \displaystyle \int \large\sf{x}^{ - 1} dx = \large \sf \: log(x) + c

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Learn more :-

∫ 1 dx = x + C

∫ sin x dx = – COS x + C

∫ cos x dx = sin x + C

∫ sec²x dx = tan x + C

∫ csc²x dx = -cot x + C

∫ sec x (tan x) dx = sec x + C

∫ csc x ( cot x) dx = – csc x + C

∫ (1/x) dx = ln |x| + C

∫ ex dx = ex+ C

∫ ax dx = (ax/ln a) + C


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