Mathematics

Solve:
$$\int {\frac{{dx}}{{x + {x^{ - 3}}}}} $$


SOLUTION
$$I=\displaystyle\int \dfrac{dx}{x+x^{-3}}$$
$$=\displaystyle\int \dfrac{x^3dx}{x^4+1}$$
Let $$x^4+1=t$$
$$4x^3dx=dt$$
$$x^3dx=\dfrac{1}{4}dt$$
$$\Rightarrow I=\dfrac{1}{4}\displaystyle\int \dfrac{dt}{t}$$
$$=\dfrac{1}{4}ln|t|+c$$
$$=\dfrac{1}{4}ln|1+x^4|+c$$.
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Subjective Medium Published on 17th 09, 2020
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