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# Problem

$\int \dfrac{\sin x + \sin^3 x}{\cos (2x) } \, dx = \,?$

Note by Brilliant Member
1 year, 1 month ago

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Hint: Start with $$y = \cos x$$, then do long division, and you get a form of $$\int \frac 1{z^2-a^2} \, dz$$. · 1 year, 1 month ago

thank you very much big brother, i am able to do it now. the answer coming is " right" · 1 year, 1 month ago

Pi Han Goh is correct , Let $$t=cosx \implies dx=\dfrac{dt}{-\sin{x}}$$

$$I=\displaystyle\int \dfrac{t^2-2}{2t^2-1}\cdot dt$$ · 1 year, 1 month ago