Question Number 214770 by MathematicalUser2357 last updated on 19/Dec/24
$$\int\mathrm{sin}^{\mathrm{3}} {xdx}=? \\ $$
Answered by mr W last updated on 19/Dec/24
$$=−\int\mathrm{sin}^{\mathrm{2}} \:{x}\:{d}\:\left(\mathrm{cos}\:{x}\right) \\ $$$$=−\int\left(\mathrm{1}−\mathrm{cos}^{\mathrm{2}} \:{x}\right)\:{d}\:\left(\mathrm{cos}\:{x}\right) \\ $$$$=−\mathrm{cos}\:{x}+\frac{\mathrm{cos}^{\mathrm{3}} \:{x}}{\mathrm{3}}+{C}\:\checkmark \\ $$
Commented by MathematicalUser2357 last updated on 19/Dec/24
$${thank}\:{you} \\ $$