Evaluate the following integral ∫(5x+3)/(2x^2+4x+3) dx
All Answers
total answers (1)
total answers (1)
Mathematics
5x+3=5/4 (4x+4)-4
need an explanation for this answer? contact us directly to get an explanation for this answer∫(5x+3)/(2x^2+4x+3) dx=5/4 ∫((4x+4))/(2x^2+4x+3)-4∫dx/(2x^2+4x+3)
2x^2+4x+3=2[(x+1)^2+1/2]
∫(5x+3)/(2x^2+4x+3) dx=5/4 ∫((4x+4))/(2x^2+4x+3)-2∫dx/((x+1)^2+1/2)
=5/4 ln〖|2x^2+4x+3|-2√2 tanh^(-1)(√2 (x+1))+c〗