Posts
Muhamad Nicky
2010 4350 1382
Kalkulus 2
1. ∫ 2- x2 dx = ∫ ( 2-x2 ) x -1/2 dx
√x
=
∫ ( 2x -1/2 – x 3/2 ) dx
= 2 x -1/2+1 -
1 x3/2+1 + C -1/2+1 3/2+1
= 2 x 1/2 - 1 x5/2
+ C
1/2 5/2
= 4x 1/2 -
2 x5/2 + C
5
2. ∫
( 1 x
+ 1 ) dx = ∫
( 1
x + x-4 ) dx
2 x4
2
= ½ x
1+1 + 1
x -4+1 + C
1+1
-4+1 = ½ x2
+ 1
x -3 + C
2
-3
-3
= ½
x2 1
x -3 + C
4
3
3. ∫
1 dx = ∫ x-3
. x -2/3 dx
x3 3√x2
= ∫ x -9/3 . x -2/3
dx
= ∫ x -11/3
= 1
x -11/3+1 + C -11 +1
3
= 1 x
-8/3 + C
-8/3 = 3 x
-8/3 + C
8
4. ∫ x
( 4x -3 ) dx =
∫
4x2 -
3x dx
 |
|||
|
|||
√x √x
= ∫ (
4x 2 -
3x ) . x -1/2 dx
=
∫
4 x 3/2 - 3x ½ dx
= 4
x 3/2+1 3 x
1/2+1 + C
3/2+1 ½+1
= 4
x 5/2 3 x
3/2 + C
5/2 3/2
= 8
x 5/2
6 x 3/2 + C 5 3
= 8
x 5/2 2 x 3/2 + C
5
5. ∫ √x –
1 + 2
dx = ∫ x 1/2 - 2x -1 + 2 x -1/2 dx
2x √x 
= 1
x 1/2+1 2 x -1+1
+ 2 x -1/2+1 + C 1/2+1 -1+1 -1/2+1
= 1
x 3/2 2 x +
2 x 1/2 + C 3/2 1/2
= 2 x 3/2 2 x +
4 x 1/2 + C
3
6. ∫ ( 2x + 3√x2 +1 ) dx = ∫ ( 2x + x2/3 +1 ) . x -1/2 dx
√x
= 2x1-1/2 + x 2/3-1/2
+ x -1/2 dx
= 2x1/2
+ x 1/6 + x -1/2 dx
= 2 x 1/2+1 +
1 x 1/6+1 + 1
x -1/2+1 dx ½ +1
1/6 +1 -1/2+1 = 2
x 3/2 + 1 x 7/6 + 1
x 1/2 dx 3/2
7/6 1/2
= 4
x 3/2 + 6 x 7/6 +
2x 1/2 + C
3 7 
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