Question

alguém consegue por favor
∫$cos^{5} xdx$

Answer 1

          $\displaystyle I=\int \cos^5 x \;dx\\ \\ \\ I=\int \cos ^4 x\cdot \cos x\;dx\\ \\ \\ I=\int \cos ^4 x\;d\sin x\\ \\ \\ I=\int (\cos ^2 x)^2\;d\sin x\\ \\ \\ I=\int (1-\sin ^2 x)^2\;d\sin x\\ \\ \\ I=\int 1-2\sin ^2 x+\sin ^4 x\;d\sin x\\ \\ \\ I=\int d\sin x-2\int \sin ^2 x\;d\sin x+\int\sin ^4 x\;d\sin x\\ \\ \\ \boxed{\boxed{I=\sin x-\dfrac{2}{3}\sin^3x+\dfrac{1}{5}\sin^5 x+C}}$