Mathematics

Evaluate $$\int {\dfrac{{{{\left( {\sin x} \right)}^{2018}}}}{{{{\left( {\cos x} \right)}^{2020}}}}\,\,dx} $$


SOLUTION
$$=\displaystyle\int \dfrac{\sin x^{2018}}{(\cos x)^{2019}}dx$$
$$=\displaystyle\int (\tan x)^{2018}\cdot \sec x^2\cdot dx$$
$$=\dfrac{1}{2019}\cdot \tan x^{2019}+c$$.
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Subjective Medium Published on 17th 09, 2020
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