询求一道不定积分题详解∫(dx/(4+9x^2 ))_数学解答

询求一道不定积分题详解
∫(dx/(4+9x^2 ))

人气：458 ℃　时间：2020-06-09 14:36:32

解答

∫(dx/(4+9x^2 ))
=（1/4）∫(dx/(1+9/4x^2 ))
=（1/4）∫(dx/(1+u^2 ))*2/3(u=3/2x)
=1/6arctanu+C=1/6arctan3/2x+C