Integrals

The value of e2e4 1x ( e (( ex)2+1 )-1e (( ex)2+1 )-1+e ((6- ex)2+1 )-1 )dx is

1. 1
2. loge 2
3. e2
4. 2

Let I(x)= dx(x-11) 1113(x+15) 1513. If I(37)-I(24)= 14 ( 1b 113- 1c 113 ), b,c N, then 3(b+c) is equal to

1. 39
2. 22
3. 40
4. 26

If I= 0 2 32x 32x+ 32x dx, then 02I x x x 4x+ 4x dx equals :

1. 212
2. 24
3. 216
4. 28

Let x3 x dx=g(x)+C, where C is the constant of integration. If 8 (g ( 2 )+g' ( 2 ) )= 3+ 2+ , , , Z, then + - equals :

1. 47
2. 55
3. 62
4. 48

Let for f(x)=7 8x+7 6x-3 4x-3 2x, I1= 0 /4f(x) dx and I2= 0 /4x f(x) dx. Then 7I1+12I2 is equal to :

1. 2
2. 1
4. 2

If x ( x -1x 1-x2+ -1x(1-x2)3/2+ x1-x2 )dx=g(x)+C, where C is the constant of integration, then g ( 12 ) equals :

1. 6 e3
2. 6 e2
3. 4 e3
4. 4 e2

Let 2 - x3 + x dx = 12 ( x + e| x + x| ) + C, where C is the constant of integration. Then + is equal to :

1. 3
2. 7
3. 1
4. 4

Let n ( n n4 + 1 - 2n (n2 + 1 ) n4 + 1 . . + n n4 + 16 - 8n (n2 + 4 ) n4 + 16 + . . + n n4 + n4 - 2n n2 (n2 + n2 ) n4 + n4 ) be k, using only the principal values of the inverse trigonometric functions. Then k2 is equal to .

The integral 1/43/4 (2 -1 1 - x1 + x ) dx is equal to

1. -1/2
2. -1/4
3. 1/4
4. 1/2

x 2 ( x3( /2)3 ( (2t1/3 ) + (t1/3 ) ) dt (x - 2 )2 ) is equal to

1. 3 22
2. 9 28
3. 5 29
4. 11 210