Evaluate the Integral. Show All Steps

Question

Evaluate the Integral. Show All Steps. If possible attach a video going through the problem

Answer 1

∫ [ (3x) / (x²+8x+21) ]dx + ∫ [2 / (x²+8x+21) ]dx

= (3/2)∫ [(2x + 8 - 8) / (x²+8x+21)]dx + ∫ [2 / ((x+4)² + 5)]dx

= (3/2)∫ [(2x+8) / (x²+8x+21)]dx - 10∫ [dx / ((x+4)² + 5) ]

= (3/2) ln l x²+8x+21 l - 2∫ [dx / ({(x+4)/√5)}² + 1)] Let u = (x+4)/√5. Then du = (1/√5)dx.

= (3/2) ln l x²+8x+21 l - 2√5 Tan^-1((x+4)/√5) + C