Mathematics

Evaluate : $$\int \dfrac{x^4+1}{x^2+1}dx$$.


SOLUTION
Given $$\int {\dfrac{x^4+1}{x^2+1}dx}$$
$$=\int {\left(\dfrac{2}{x^2+1}+x^2-1\right)dx}$$
$$=2\int{\dfrac{1}{x^2+1}dx}+\int{x^2 dx}-\int{1dx}$$
$$=2(\tan^{-1}x)+\dfrac{x^3}{3}-x+C$$
$$=2\tan^{-1}x+\dfrac{x^3}{3}-x+C$$
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Subjective Medium Published on 17th 09, 2020
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