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Chapter 5: Q. 53 (page 465)

Solve the integral

鈭�1x2-4x+13dx

Short Answer

Expert verified

13tan-1(13(x-2)+C

Step by step solution

01

Step 1. Given

鈭�1x2-4x+13dx

02

Step 2. Calculation

鈭�1x2-4x+13dx=1(x-2)2+9dx=1(u)2+9[u=x-2,du=dx]=鈭�13(v2+1)dv=13鈭�1(v2+1)dv=13tan-1(v)+C=13tan-1(u3)+C=13tan-1(13(x-2)+C

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