Trigonometric Reduction Formulas

Reference > Calculus: Integration

 Description$$\int \sin^{n}x \, dx=-\frac{1}{n}\sin^{n-1}x\cos{x}+\frac{n-1}{n}\int \sin^{n-2}x \, dx$$ $$\int \cos^{n}x \, dx=\frac{1}{n}\cos^{n-1}x\sin{x}+\frac{n-1}{n}\int \cos^{n-2}x \, dx$$ $$\int \tan^{n}x \, dx=\frac{1}{n-1}\tan^{n-1}x-\int \tan^{n-2}x \, dx$$ $$\int \cot^{n}x \, dx=-\frac{1}{n-1}\cot^{n-1}x-\int \cot^{n-2}x \, dx$$ $$\int \sec^{n}x \, dx=\frac{1}{n-1}\sec^{n-2}x\tan{x}+\frac{n-2}{n-1}\int \sec^{n-2}x \, dx$$ $$\int \csc^{n}x \, dx=-\frac{1}{n-1}\csc^{n-2}x\cot{x}+\frac{n-2}{n-1}\int \csc^{n-2}x \, dx$$