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

Answered by Frix last updated on 23/Jan/25

$$\int {(\cos x+\sin x)}^n(1-{2\sin }^{2}x)dx=$$$$=\int {(\cos x+\sin x)}^n({\sin }^{2}x-{\cos }^{2}x)dx=$$$$=\int {(\cos x+\sin x)}^{n+1}(\sin x-\cos x)dx=$$$$=\frac{1}{n+2}{(\cos x+\sin x)}^{n+2}+C$$

Commented by mehdee7396 last updated on 23/Jan/25

$$\underset{―}{\underbrace{⋚}}$$

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