`int(dx)/(cosx+sqrt(3)sinx)` equals: (1) `1/2logtan(x/2+pi/(12))+c` (2) `1/2logtan(x/2-pi/(12))+c` (3) `logtan(x/2+pi/(12))+c` (4) `logtan(x/2-pi/(12))+c`

int1/(cosx+sqrt(3)sinx)\ dx is equal to (a) logtan(pi/3+x/2)+C (b) logtan(x/2-pi/3)+C (c) 1/2logtan(x/2+pi/3)+C (d) none of these

intdx/(cosx-sinx) is equal to (A) 1/sqrt(2)log|tan(x/2-(3x)/8)|+C (B) 1/sqrt(2)log|cot(x/2)|+C (C) 1/sqrt(2)log|tan(x/2-pi/6)|+C (D) 1/sqrt(2)log|tan(x/2+(3pi)/8)|+C

Evaluate: int(cosecx)/(logtan(x/2))dx

int_1^(sqrt(3))1/(1+x^2)dx is equal to a. pi/(12) b. pi/4 c. pi/6 d. pi/3

int_0^3(3x+1)/(x^2+9)dx = (pi^)/(12)+log(2sqrt(2)) (b) (pi^)/2+log(2sqrt(2)) (c) (pi^)/6+log(2sqrt(2)) (d) (pi^)/3+log(2sqrt(2))

int_0^(pi^2//4)(sinsqrt(x))/(sqrt(x))dx equals a. pi^2//8 b. pi//4 c. 2 d. 1

If y=(x^4-x^2+1)/(x^2+sqrt(3)x+1) and (dy)/(dx)=a x+b , then the value of a+b is (a) cot(pi/8) (b) cot((5pi)/12) (c) tan((5pi)/12) (d) tan((5pi)/8)

int_0^(pi//2)(sinx)/(sin x+cos x)dx equals to a. pi//2 b. pi//4 c. pi//3 d. pi

If both roots of quadratic equation x^2+(sintheta+costheta)x+3/8=0 are positive and distinct then complete set of value of theta in [0,2pi] is (1) (pi/(12),(5pi)/(12)) (2) ((13pi)/(12),(17pi)/(12)) (3)((7pi)/(12),(11pi)/(12)) (4) ((19pi)/(12),(23pi)/(12))

Choose the correct answer int1sqrt(3)(dx)/(1+x^2) equals (A) pi/3 (B) (2pi)/3 (C) pi/6 (D) pi/(12)