224
CHAPTER 27
27.32
27.33
27.34
27.35
27.36
27.37
27.38
27.39
What identity is implied by the result of Problem 27.35?
Two functions with the same derivative differ by a constant. Hence, tan ' [(a + x)/(l — ax)] = tan ' x +
C. When x = 0, tan"
1 a = tan~
l O+ C = 0 + C= C. Thus, the identity is tan"' [(a + *)/(! - ax)] =
tan"
1 x + tan"
1 a.
In Problems 27.39-27.57, evaluate the indicated antiderivative.
special case of the formula
This is a
for x> 1
for x<-l
y= In (tan ' x).
y = esc '
y = jcva" — x
2 + a
2 sin ' (x/a), where a > 0.
y = tan
y = sin
sec ' x.
y = tan '
Let x = 2u, dx = 2 Then