`1/2x+1/3(x+2)+1/4(x+7)=x`

Without expanding, find the value of: (i) (x + 1)^4 - 4(x + 1)^3 (x - 1) + 6(x + 1)^2 (x - 1)^2 - 4(x + 1) (x - 1)^3 + (x -1)^4 (ii) (2x - 1)^4 + 4(2x - 1)^3 (3 - 2x) + 6(2x - 1)^2 (3 - 2x)^2 + 4(2x - 1) (3 - 2x)^3 + (3 - 2x)^4

int (2x ^ (3) + 3x ^ (2) + 4x + 5) / (2x + 1) dx equls to: (A) (x ^ (3)) / (2) + (x ^ (2)) / (2) +3 (x) / (2) + (7) / (4) ln (2x + 1) + C (B) 5 (x ^ (3)) / (2) + 6 (x) / (2) + (7) / (4) ln (2x + 1) + C (C) 3 (x ^ (3)) / (2) + 3 (x ^ (2)) / (2) + (7 ) / (4) ln (2x + 1) + C (D) (x ^ (2)) / (2) + 3 (x) / (2) + (7) / (4) ln (2x + 1) + C

Solve each of the following equations and also check your result in each case: 1) 1/2x+7x-6=7x+1/4 2) 3/4x+4x=7/8+6x-6 3) 7/2x-5/2x=(20)/3x+10 (4) (6x+1)/2+1=(7x-3)/3

Solve the following equations for x:4^(2x)=(1)/(32)( ii) 4^(x-1)x(0.5)^(3-2x)=((1)/(8))^(x)2^(3x-7)=256

If x+1/x=3, calculate x^2+1/(x^2),\ x^3+1/(x^3) and x^4+1/(x^4)

(7 ^ (2x + 3) + 7 ^ (2x + 1)) / (7 ^ (2x + 2) + 7 ^ (2x + 1))

7x-1 / 4-1 / 3 (2x-1-x / 2) = 10/3

If x ^(3) - 7x + 4 is divided by (x-1), (x +2) and (2x +1), then the find the respective remainders.

Add: (3x^(2) - (1)/(5)x + (7)/(3)) + ((-1)/(4)x^(2) + (1)/(3)x - (1)/(6)) + (-2x^(2) - (1)/(2)x + 5)