Woods, Frederick S. (Frederick Shenstone), 1864-, Bailey, Frederick H. (Frederick Harold), 1865- · Boston, New York [etc.] Ginn and Company · leaf 247
= sin2 2 x (cos 2 x dx)and placing sin 2 x = u, we have / sin22 x cos 2 xdx = £ j u9<£« = J sin3 2 x.Combining these results, we have, finally, f sin2x cos4x</x = rV x + ?V s*n3 - x — sV s*n4 x + C. 230 INTEGRATION Ex. 8. Find the value of J Vl + cosxdx.Since cos x = 2 cos- - Therefore 113.… … / VI - ulu i /. 1 + wdu = sin m or - cos-1w,= tan-1?/or — ctn-1w, sec u or mVm2 — 1 These formulas are much more serviceable, however, if u is ureplaced by - (a> 0). Making this substitution and evident reductions, we have as our required formulas du , u _,N = sin 1 -, (1) / Va2 - u2 a f du 1…
Geometry, Analytic · Calculus
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