Gilbert Strang

Question

$\int_{0}^{1}(x^2+1)^4dx$

Comments

take x=tany then 1+tany^2=(secy^2)^2
now the question is  integrate 1/{cosy^4}  which can be easily solve by substitution method and change value of limit also from pi/2 pi/4

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What about applying binomial theorem:

It gives answer = $\frac{1}{9}+\frac{4}{7}+\frac{6}{5}+\frac{4}{3}+1+C$