(a(i))[3]
With the substitution $u = 1 + x^2$, show that $I = \int_1^2 \frac{(u - 1)^2}{2u^3}\,du$.
(a(ii))[5]
Hence determine the exact value of $I$.
Mathematics 9709 · AS & A Level · Integration
Integration — practice question
Define $I = \int_0^1 \frac{x^5}{(1 + x^2)^3}\,dx$.