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sin-3-xdx-




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

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