Question

You are given the following integral: St 2. - 4 ·da 22 +1 On a piece of paper evaluate this integral. Use your working to choose from the options below: Steps to evaluate this integral would require: A Substituting u = :22 - 4, B. Factorising a? +1 and then splitting the integrand into partial fractions, C. Rewriting the numerator of the integrand as }(4x - 8), D. Splitting integrand into * - ** E Substituting u F. The answer is In (2+ 1) + G. The answer is in (2:+1)+c, H. The answer is In(?+ 1) - 4 arctan(x? + 1) + 1. The answer is In(x? + 1) - 4 arctan(x) + 2+1

Answer 1

I = 2.c 4 -dz 2 +1 2.c 4 -]d.c 12+1 x² + 20 -do 4 c2 +1 22 +1 2.c 11 -d.c ..? 2+1 Substitute : u= x2 +1 1 du = (2x + 0) * d.c du 2x + da 11 - 1 du -du = ln(u) +C 11 = In (x2 + 1) +C 12 Jati * dt = arctan (2) + 2+1 So, I = 11 -4*12 I = ln (.x2 + 1) – 4 * arctan (2) +C

So steps used are D and I

Let me know if you've any query.