Question Number 215963 by RoseAli last updated on 23/Jan/25

Answered by Frix last updated on 23/Jan/25

$$\int\left(\mathrm{cos}\:{x}\:+\mathrm{sin}\:{x}\right)^{{n}} \left(\mathrm{1}−\mathrm{2sin}^{\mathrm{2}} \:{x}\right){dx}= \\ $$$$=\int\left(\mathrm{cos}\:{x}\:+\mathrm{sin}\:{x}\right)^{{n}} \left(\mathrm{sin}^{\mathrm{2}} \:{x}\:−\mathrm{cos}^{\mathrm{2}} \:{x}\right){dx}= \\ $$$$=\int\left(\mathrm{cos}\:{x}\:+\mathrm{sin}\:{x}\right)^{{n}+\mathrm{1}} \left(\mathrm{sin}\:{x}\:−\mathrm{cos}\:{x}\right){dx}= \\ $$$$=\frac{\mathrm{1}}{{n}+\mathrm{2}}\left(\mathrm{cos}\:{x}\:+\mathrm{sin}\:{x}\right)^{{n}+\mathrm{2}} +{C} \\ $$
Commented by mehdee7396 last updated on 23/Jan/25

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