`int_(-2)^0{x^3+3x^2+3x+3+(x+1)cos(x+1)dx` is equal to (A) -4 (B) 0 (C) 4 (D) 6

int (x^2 -1 )/ (x^3 sqrt(2x^4 - 2x^2 +1))dx is equal to

int_0^oo(x dx)/((1+x)(1+x^2)) is equal to (A) pi/4 (B) pi/2 (C) pi (D) none of these"

int_(5/2)^5(sqrt((25-x^2)^3))/(x^4)dx is equal to (a) pi/6 (b) (2pi)/3 (c) (5pi)/6 (d) pi/3

("lim")_(xvecoo)(sin^4x-sin^2x+1)/(cos^4x-cos^2x+1) is equal to (a) 0 (b) 1 (c) 1/3 (d) 1/2

lim_(xvecoo)((x^2+2x-1)/(2x^2-3x-2))^((2x+1)/(2x-1)) is equal to (a) 0 (b) oo (c) 1/2 (d) none of these

Let f: R->R be a continuous function and f(x)=f(2x) is true AAx in Rdot If f(1)=3, then the value of int_(-1)^1f(f(x))dx is equal to (a)6 (b) 0 (c) 3f(3) (d) 2f(0)

int sqrt(x)(1+x^(1//3))^(4)dx " is equal to "

The equation of the curve is y=f(x)dot The tangents at [1,f(1),[2,f(2)],a n d[3,f(3)] make angles pi/6,pi/3,a n dpi/4, respectively, with the positive direction of x-axis. Then the value of int_2^3f^(prime)(x)f^(x)dx+int_1^3f^(x)dx is equal to (a) -1/(sqrt(3)) (b) 1/(sqrt(3)) (c) 0 (d) none of these

If int (x^(6)+7x^(5)+6x^(4)+5x^(3)+4x^(2)+3x+1)e^(x)dx is equal to sum_(k=1)^(alpha) betax^(k).e^(x)+C (where C is constant of integration) then (alpha + beta) is

int(x+x^(2/3)+x^(1/6))/(x(1+x^(1/3)))dx equals