1 Integralni racun - zadaci za zagrijavanje

Svodeci na tablicne izracunati sljedece integrale

1.

(x2 + x +

1

x+ sinx

)dx

2.

x3 + x 2

xdx

3.

6x4 + 8x

72 5x + 2x

dx

4.

(x + 1)(x2 3)

3x2dx

5.

(x

x)(1 +

x)

3x

dx

6.

(2

1 + x2 3

1 x2

)dx

7.

ax(

1 +ax

cos2 x

)dx

8.

3x + 5x

2x+1dx

9.

1

sin2 x cos2 xdx

10.

(sin

x

2 cos x

2

)2dx

1

Rjesenja:

1.x3

3+

x2

2+ ln |x| cosx + c

2.x3

3+ x 2 ln |x|+ c

3. 6x4

4+

16

7x

72 5x + 2 ln |x|+ c

4.x2

6 ln |x|+ 1

3x +

1

x+ c

5.6

13x

136 +

6

7x

76 + c

6. 2 arctanx 3 arcsinx + c

7.ax

ln a+ tanx + c

8.1

2

( 32 )x

ln 32+

1

2

( 52 )x

ln 52+ c

9. tanx cotx + c

10. x + cosx + c

Eventualne greske prijaviti na mail vanja@etfbl.net.

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