Question Number 102461 by bemath last updated on 09/Jul/20

∫ (dx/(√(5e^(2x) +4e^x +1))) =?

Answered by PRITHWISH SEN 2 last updated on 09/Jul/20

∫(dx/(e^x (√((1/e^(2x) )+(4/e^x )+5))))   put (1/e^x ) = t⇒(dx/e^x ) = −dt  = −∫(dt/((√(t^2 +4t+5)) )) = −∫(dt/(√((t+2)^2 +1)))  =−ln∣(t+2)+(√(t^2 +4t+5))∣ +C  =ln∣(e^x /(2e^x +1+(√(5e^(2x) +4e^x +1))))∣+C  please check.