Problem - 4615
Compute $$\int\sin^5{x}dx$$
$$\int\sin^5{x}dx=-\int\sin^4{x}d(\cos{x})=-\int(1-\cos^2{x})^2d(\cos{x})=-\int(1-2\cos^2{x}+\cos^4{x})d(\cos{x})=\boxed{-\cos{x}+\frac{2}{3}\cos^3{x}-\frac{1}{5}\cos^5{x}+C}$$
Compute $$\int\sin^5{x}dx$$
$$\int\sin^5{x}dx=-\int\sin^4{x}d(\cos{x})=-\int(1-\cos^2{x})^2d(\cos{x})=-\int(1-2\cos^2{x}+\cos^4{x})d(\cos{x})=\boxed{-\cos{x}+\frac{2}{3}\cos^3{x}-\frac{1}{5}\cos^5{x}+C}$$