∫dx8+3x−x2 is equal to

LetI=∫18+3x−x2dx=∫18−x2−3x+322−322dx=∫18−x−322−94dx=∫18+94−x−322dx=∫14122−x−322dxLet x−32=t⇒dx=dt∴I=∫14122−t2dt=sin−1⁡t412+C∵∫dxa2−x2=sin−1⁡xa=sin−1⁡x−32412+C=sin−1⁡2x−341+C∵t=x−32