7/23/2019 buat-buat

1/3

1. Dik :

x

dzz )exp(2

=erf(x)-1=erfc(x)2

Dit : buktikan

=x x

x

dzzzx

edzz )exp(21

2)exp( 2

2

2

2

Jawab :

2.

+

dx

xx 569

1

2

Jawab :

+

dx

xx 569

1

2 ( )

++

dx

xx 4169

1

2

( )92

6+= xu

=

dx

xx

+

+

9

4

9

1

9

6

1

2

3

1= x

=

dx

x

+

9

4

3

1

1

2

dxdu==

du

u

+9

4

1

2

+

du

9

4tan

9

4

1

2

Misal :

tan3

2=u

=

dsec

3

2

sec3

2 2

dsec3

2 2=du

=

dsec

7/23/2019 buat-buat

2/3

=

( ) tansecln ++c

=

+

+2

3

2

49ln

2uu

+c

3.

=

=

Cn

Co

kCn

Co

k

n

n

n

ln1

1lim

1

Jawab :

4.

( )dx

x

x

122

Jawab :

( )dx

x

x

122

dtansec

1sec

sec

2

2

sec=x=

d 2

3

tan

tansec

dtansec=dx=

d tan

sec3

=

( )

d +tan

1tansec 2

=

dd +

tan

sec

tan

tansec 2

=

d

+

sin

1dtansec

7/23/2019 buat-buat

3/3

=

+ dcscsec

=

( )( ) cotcscln ++x

+c

=

+

+

1

1

1

ln22

xx

xx

+c

=

+

1

1ln

2x

xx

+c