An Elementary Treatise of the Differential And Integral Calculus

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1 + xi y = p^ — 2x — fa;^ + Bxi + 2x^ — 6xi — 6x^ + 6 log {xi + 1) + 6 tan-ia;i • , 3a;4 - 3xi , 3- dy = —^ ^dx.
3x^ + x^ y = 12 (fa;* — fa;* + ^-^^^ — 9«*) + 1908 [^a;A— |a;^+3a;i— ^a;^ + 81a;A— 343 log(a;A+3)].
EXAMPLES.
281 4. ay = — ! — - dx.
1 + xi a;" 4 +|- + ilog(l+:r*) (Art. 142.) 5. dy = xdx (1 + #■ Vl +X + Vl + a;J (?a; a^Va + 5a; va '\fx 7. % = Ja; (1 + x)i + (1 + !r)^ y = 3 tan-i (1 + a;)4.
8. dy = 4:{x + Vx + S + ^/x + 3)dx.
y = 2 {x + By—12{x + 3) + %(x+g)i + 3 {x+3)t (Art. 143.)
...9-m JjlAltK • dy = -^:==3 V 1 + X 10. % = 11, dy = y = i{l + a;3)t - | (1 + a^^)* + (1 + ^)^- 3?dx 3x> + 2 (1 + a:2)t o^dx (1 + a;8)t" 2^= - 3 (1 + a;")' ■v/l + a?' 282 EXAMPLES.
12. dy = ^^ (Art. 144.) ■s/l + X + x> y = log (l + 2a; + 2\/l + x + a?).
(See Art. 144, Ex. 1.) 13. dy = Vx^ — x—1 y = log (2a; — 1 + 2'\/a;2 — x — 1).
14. e?tf = ,— - =^- y = —2 tan-U /— ^ 15. dy = — X 2' Vl +X — '.
2, = -2 tan- V^^^-^^^ 16. dy = x-i- i-v/5 dx (Assume \/^ + x' = z — x, etc.


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