Evaluate : (i) `(3x + (1)/(2) ) (2x + (1)/(3) )`

Evaluate: (i) int(3x+1)/((3x^2+2x+1)^3)\ dx (ii) intsin^3xcosx\ dx

If x=3+2sqrt(2) , find : (i) (1)/(x) (ii) x-(1)/(x) (iii) (x-(1)/(x))^(3) (iv)x^(3)-(1)/(x^(3))

Evaluate: (i) int(x^2+3x-1)/((x+1)^2)\ dx (ii) int(2x-1)/((x-1)^2)\ dx

Find the value of x and y (1)/(2x)+(1)/(3y)=2 (1)/(3x)+(1)/(2y)=(13)/(6)

Evaluate: int(3x^2+2x+1)/(x^2+x+1)dx

Evaluate: (i) int(x^2+x+5)/(3x+2)\ dx (ii) int(2x+3)/((x-1)^2)\ dx

Evaluate: (i) intsqrt((1-sin2x)/(1+sin2x))\ dx (ii) int(e^(3x))/(e^(3x)+1)\ dx

Evaluate: int(x^3+3x+2)/((x^2+1)^2(x+1))dx

Find the derivative (i) x^(1//3) (ii) (2)/(x^(3//2)) (iii) 3x^(-1//4)

Find the remainder when x^(3)+3x^(2)+3x+1 is divided by : (i) x+1 " " (ii) x-(1)/(2) " " (iii) x " " (iv) x+pi " " (v) 5+2x