Mathematics

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


SOLUTION
Now,
$$\displaystyle\int\dfrac{1}{x^{1-n}(1+x^{2n})}dx$$
$$=\displaystyle\int\dfrac{x^{n-1}}{(1+x^{2n})}dx$$
$$=\dfrac{1}{n}\displaystyle\int\dfrac{d(x^{n})}{(1+(x^{n})^2)}dx$$
$$=\dfrac{1}{n}\tan^{-1}x^n+c$$ [ Where $$c$$ is integrating constant]
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Subjective Medium Published on 17th 09, 2020
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