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Summary - Introduction To Calculas
- Course
- Introduction To Calculas
- Institution
- University Of Johannesburg (UJ)
this document is the tutorial work which covers intergration by parts and reduction formulas
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MATH141 TUT 3The tutorial questions for each week are recommended problems. It is in your own interest
to work out as many as of the remaining problems of the exercises in the prescribed textbook
out as possible.
Standard Integrals and u-Substitution - Exercise 7.1
1. Evaluate the following integrals by making appropriate u-substitution and applying
standard integrals:
(a)
Z
cot2 x + 1dx
(b)
Z
2x + 1
dx
x2 + 1
(c)
Z
e2x+1 dx
(d)
Z
1
dx
(ex + e−x )2
(e)
Z
1
dx
csc x
(f)
Z
1
dx
cos2 x
(g)
Z
(6 − 2x)2 dx
(h)
√
Z
4 + 9xdx
(i)
Z
2x sec(x2 )dx
(j)
√
Z
cos x sin xdx
1
, (k)
Z
cos 3x
dx
2 + sin 3x
(l)
Z
x tan2 (x2 ) sec2 (x2 )dx
(m)
Z
e3 tan x sec2 xdx
(n)
Z
x
√ dx
4 1 − x2
(o)
Z
cos x
√ 2 dx
sin x sin x + 4
(p)
ex
Z
√ dx
9 + e2x
(q)
−1
etan x
Z
dx
1 + x2
(r) √
e x−2
Z
√ dx
x−2
(s)
Z
dx
dx
x ln x
(t)
Z
dx
√ √x dx
x5
(u)
Z
sin(ln x)
dx
x
(v)
ex
Z
√ dx
9 − e2x
(w)
Z
2
x5−x dx
2
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