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What is int tanxtan2xtan3x dx is equal to

Given: ∫tanx.tan2x.tan3x dx Solution: tan(3x)=tan(x+2x) tan(3x)=tanx+tan2x/1-tanx.tan2x tan(3x)-tanxtan(2x)tan(3x)=tanx+tan(2x) Therefore, tanx.tan(2x)tan(3x)=tan(3x)-tan(x)-tan(2x) ∫tanx.tan2x.tan3x dx ∫tan(3x)-tan(x)-tan(2x).dx =1/3log|sec(3x)|-log|secx|-1/2log|sec(2x)|+C