Understanding Engineering Mathematics

(iv)

ex

2

(cosx+sinx) (v) x^2 sinx+ 2 xcosx−2sinx

(vi)

x^2

2

ln|x|−

x^2

4

(vii)

1

2

(x^2 − 1 )ex

2

9.3.11 Choice of integration methods

A.(i) A (ii) C (iii) B (iv) B (v) A (vi) B

B.(i) B, C (ii) A, C (iii) C (iv) C (v) B, C (vi) B, C

C. (i) ln|x^2 − 6 x+ 4 | (ii)

cos^3 x

3

−cosx (iii) x

(iv)

1

2

ln( 2 x+ 3 )

(v)

1

6

e^3 x

2

(vi) 3 sin−^1

(

x+ 1

2

)

(vii) −xcos(x+ 1 )+sin(x+ 1 )

(viii)

3

8

x+

1

4

sin 2x+

1

32

sin 4x (ix)

x^2

2

−xlnx+x

(x) 5 ln(x− 3 )−4ln(x− 2 ) (xi)

1

4

e^2 x( 2 x− 1 ) (xii) sin(ex)

(xiii) −

1

8

cos 4x (xiv)

√

x^2 − 2 x+ 3

(xv)

1

2

ln(x^2 + 2 x+ 2 )+2tan−^1 (x+ 1 )

(xvi)

1

18

(9cosx−cos 9x) (xvii)

1

2

sin(x^2 + 1 )

9.3.12 The definite integral

A.(i)

1

3

(ii)

π

2

− 1 (iii)

2

3

(

√

2 − 1 ) (iv) 2 ln 3−3ln2 (v) 1