Mathematics

Integrate $$\displaystyle \int \cos^3x \ dx$$


SOLUTION
Consider $$I=\displaystyle \int \cos^3 x \ dx$$

$$I=\displaystyle \int \dfrac{\cos 3x+3\cos x}{4} \ dx$$      $$[\because cos3A=\left( 4\cos ^{ 3 }{ A } -3\cos { A }\right)]$$ 

$$I=\displaystyle \dfrac{1}{4}\int \cos 3x +3\cos x \ dx$$

$$I=\displaystyle \dfrac{1}{4}\int \cos 3x\ dx +\dfrac{1}{4} \int 3\cos x \ dx$$

$$I=\displaystyle \dfrac{1}{4}\left[\dfrac{\sin 3x}{3}+3\sin x\right]+C$$
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Subjective Medium Published on 17th 09, 2020
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