dx/(e^x+4e^-x+3)
问题描述:
dx/(e^x+4e^-x+3)
求不定积分
答
∫dx/[e^x+4e^(-x)+3]=∫e^xdx/[e^(2x)+3e^x+4]
=∫d(e^x)/[(e^x+3/2)²+(√7/2)²]
=(2/√7)arctan[(e^x+3/2)/(√7/2)]+C (C是任意常数)
=(2√7/7)arctan[(2e^x+3)/√7]+C.