Question Number 215414 by MATHEMATICSAM last updated on 06/Jan/25
$$\int\:\frac{\mathrm{sin}^{\mathrm{3}} \left(\frac{{x}}{\mathrm{2}}\right)\mathrm{sec}\left(\frac{{x}}{\mathrm{2}}\right)}{\:\sqrt{\mathrm{cos}^{\mathrm{3}} {x}\:+\:\mathrm{cos}^{\mathrm{2}} {x}\:+\:\mathrm{cos}{x}}}\:{dx} \\ $$$$\mathrm{Solve}\:\mathrm{this}\:\mathrm{integral}. \\ $$
Commented by JamesZhou last updated on 06/Jan/25
$${maybe}\:{numerator}\:{issi}\hat {{n}}\mathrm{3}… \\ $$
Commented by MATHEMATICSAM last updated on 06/Jan/25
$$\mathrm{yes}.\:\mathrm{corrected} \\ $$
Answered by MathematicalUser2357 last updated on 06/Jan/25
$$\frac{{x}^{\mathrm{3}} }{\mathrm{12}\sqrt{\mathrm{3}}}+\frac{\mathrm{13}{x}^{\mathrm{5}} }{\mathrm{480}\sqrt{\mathrm{3}}}+\frac{\mathrm{1111}{x}^{\mathrm{7}} }{\mathrm{161280}\sqrt{\mathrm{3}}}+\ldots+{C} \\ $$$$ \\ $$
Answered by JamesZhou last updated on 06/Jan/25
