Solve all Q24 explaining detailly each step Transcribed Image Text: 2x+3
20. a) Evaluate ,
dx, leaving your answer in terms of natural logarithms.
b) Find f
dx
4-4sine
21. using the substitution x = cost, evaluate fi
dx
xV1-x
22. Find (i) f xe-x* dx
(ii) Evaluate lx – 3 dx
(iii) Use the substitution x = 2(1 + cos e) to show that dx=
23.(i) Find f Inxdx (ii) Evaluate f** dx using the substitution UƯ² =1 + 2x
Vi+2x
x+1
24. (i) Find
a) cos3x cos5xdx
b) S xln 2x dx(
2×2+8
25. Evaluate
dx leaving your answer in terms of natural logarithm:
1 (x-3)(x2+1)
26. Evaluate f
xcosx dx.
x+1
27. i) f(x)=
(x-2) (x+3)
a) Express f(x) in partial fractions.
b) Find f(x)dx, leaving your answer in terms of natural logarithms.
ii) Find fx sin 2x dx
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