第2006题：万能公式代换
计算不定积分∫dx3+sinx \int \dfrac{dx}{3+\sin x}∫3+sinxdx .
A. 33arctan33(tanx2+23)\dfrac{\sqrt{3}}{3} \arctan \dfrac{\sqrt{3}}{3}(\tan{\dfrac{x}{2}+\dfrac{2}{3}})3√3arctan3√3(tan2x+32) +C+C+C
B. 22arctan324(tanx2+13)\dfrac{\sqrt{2}}{2} \arctan \dfrac{3\sqrt{2}}{4}(\tan{\dfrac{x}{2}+\dfrac{1}{3}})2√2arctan43√2(tan2x+31) +C+C+C
C. 233arctan233(tanx2+23)\dfrac{2\sqrt{3}}{3} \arctan \dfrac{2\sqrt{3}}{3}(\tan{\dfrac{x}{2}+\dfrac{2}{3}})32√3arctan32√3(tan2x+32) +C+C+C
D. 322arctan322(tanx2+13)\dfrac{3\sqrt{2}}{2} \arctan \dfrac{3\sqrt{2}}{2}(\tan{\dfrac{x}{2}+\dfrac{1}{3}})23√2arctan23√2(tan2x+31) +C+C+C
提示，令 u=tanx2u=\tan \dfrac{x}{2}u=tan2x ，利用三角函数万能公做代换.
安卓手机扫描二维码安装App
苹果手机扫描二维码安装App