190 Chapter 6Methods of integration
72.If , show that (Equation (6.33))
Evaluate by means of the substitution t 1 = 1 tan 1 θ 22 :
Section 6.7
76.By differentiation of the integral
with respect to a, show that
Z
0
2
1
2
135 2 12
∞
xe dx
n
a
a
naxnn−
+
=
⋅⋅()− π
Z
0
2
12
∞
edx
a
−ax=
π
Z
dθ
1 ++sin cosθθ
Z
dθ
53 − cosθ
Z
dθ
cosθ
d
t
θ= dt
2
1
2
t=tan
θ
2
Z
43
45
22
x
xx
dx
()++
Z
x
xx
dx
2
++ 45
Z
dx
()xx
22
++ 45
Z
dx
xx
2
++ 45
Z
x
xx
dx
()( )
22
++ 34
Z
x
xx
dx
++
2
45