Mathematics

Integrate :-
 $$\displaystyle \int_{}^{} {\frac{{dx}}{{x\left( {x + 1} \right)}}} $$ 


SOLUTION
$$=\int \frac{dx}{x(x+1)}$$
= Breaking it into partial fractions.
$$\int \frac{dx}{x(x+1)}= A\int \frac{dx}{x}+ B\int \frac{dx}{x+1}$$
$$1=A(x+1)+Bx$$
Put x=0,    put x=-1
A=1           B=-1
$$log |x|-log |x+1|+c$$
$$= log |\frac{x}{x+1}|+c$$

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Subjective Medium Published on 17th 09, 2020
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