∫dx(x+2)x2+1is equal to

Let 1(x+2)x2+1=Ax+2+Bx+Cx2+1⇒ 1=Ax2+1+(Bx+C)(x+2)Put  x=−2, we get A=15Now, comparing the coefficients of x2 and constant term,we get0=A+Band 1=A+2C⇒ B=−15,C=25So, I=15∫dxx+2−15∫xx2+1dx+25∫dxx2+1=15log⁡|x+2|−110log⁡x2+1+25tan−1⁡x+C