Substitution:
x=52secθ
Then dx=52cos2θsinθdθ
∫25x2−4dx=∫52cos2θ4sec2θ−4sinθdθ=51∫cos2θsec2θ−1sinθdθ=
=51∫cos2θtanθsinθdθ=51∫cosθdθ=51∫secθdθ=51ln∣secθ+tanθ∣+C.http://www.math.com/tables/integrals/more/sec.htm
secθ=25x
x2=254cos2θ1x2−254=254tan2θtan2θ=425x2−1tanθ=425x2−1
We have
∫25x2−4dx=51ln∣25x+425x2−1∣+C.
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