Mathematics

Evaluate :
$$\int \dfrac{(1+\log x)^2}{x} \ dx$$


SOLUTION
Let $$I=\int \dfrac{(1+\log x)^2}{x} \ dx$$

Let $$1+\log x=t$$
$$\dfrac{1}{x} \ dx=dt$$

Putting $$1+\log x =t$$ and $$dx = x \ dt$$, we get,
Therefore,
$$I=\int \dfrac{t^2}{x} \times x \ dt$$

$$I=\dfrac{t^3}{3}+C$$

$$I=\dfrac{(1+\log x)^3}{3}+C$$
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Subjective Medium Published on 17th 09, 2020
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