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

Note by Brilliant Member 10 months, 1 week ago

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Hint: Start with \( y = \cos x\), then do long division, and you get a form of \( \int \frac 1{z^2-a^2} \, dz \). – Pi Han Goh · 10 months, 1 week ago

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@Pi Han Goh – thank you very much big brother, i am able to do it now. the answer coming is " right" – Brilliant Member · 10 months, 1 week ago

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

\(I=\displaystyle\int \dfrac{t^2-2}{2t^2-1}\cdot dt\) – Sambhrant Sachan · 10 months, 1 week ago

@Sambhrant Sachan – yeah i totally agree with you and pi han goh . thanks for seeing to it, plz keep supporting. – Brilliant Member · 10 months, 1 week ago

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TopNewestHint: Start with \( y = \cos x\), then do long division, and you get a form of \( \int \frac 1{z^2-a^2} \, dz \). – Pi Han Goh · 10 months, 1 week agoLog in to reply

– Brilliant Member · 10 months, 1 week ago

thank you very much big brother, i am able to do it now. the answer coming is " right"Log in to reply

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

\(I=\displaystyle\int \dfrac{t^2-2}{2t^2-1}\cdot dt\) – Sambhrant Sachan · 10 months, 1 week ago

Log in to reply

– Brilliant Member · 10 months, 1 week ago

yeah i totally agree with you and pi han goh . thanks for seeing to it, plz keep supporting.Log in to reply