Mathematics

Find :
$$\int {\log xdx} $$


SOLUTION
$$\int \log x dx$$

Now,
we can also write 
$$\int \log x\times 1 dx$$

it is in from of partial fraction


$$\int u\times v=u\int v dx-\int[\dfrac{du}{dx}\times \int v dx]dx$$

$$=>\log x\int 1dx-\int[\dfrac{d\log x}{dx}\times \int 1 dx]dx$$

$$=>\log x\times x-\int [\dfrac{1}{x}\times x]dx$$

$$=>x\log x-\int1dx$$
$$=>x\log x-x+c$$
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Subjective Medium Published on 17th 09, 2020
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