=sqrt(3x+2)+(1)/(sqrt(2x^(2)+4))+(cos x)^(tan x)

IfI=int(dx)/(x^(3)sqrt(x^(2)-1)), then Iequals a.(1)/(2)((sqrt(x^(2)-1))/(x^(3))+tan^(-1)sqrt(x^(2)-1))+C b.(1)/(2)((sqrt(x^(2)-1))/(x^(2))+x tan^(-1)sqrt(x^(2)-1))+Cc(1)/(2)((sqrt(x^(2)-1))/(x^(2))+tan^(-1)sqrt(x^(2)-1))+Cd(1)/(2)((sqrt(x^(2)-1))/(x^(2))+tan^(-1)sqrt(x^(2)-1))+C

If I=int(sin x+sin^(3)x)/(cos2x)dx=P cos x+Q log|f(x)|+R then (a)P=(1)/(2),Q=-(3)/(4sqrt(2))(b)P=(1)/(4),Q=(1)/(sqrt(2)) (c) f(x)=(sqrt(2)cos x+1)/(sqrt(2)cos x-1)(d)f(x)=(sqrt(2)cos x-1)/(sqrt(2)cos x+1)

int_(-(1)/(sqrt(3)))^(-(1)/(sqrt(3)))(x^(4))/(1-x^(4))cos^(-1)((2x)/(1+x^(2)))dx

Prove that tan ^(-1) ((sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2)))=pi/4+1/2 cos ^(-1) x^2

Differentiate tan^(-1)((sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2))+sqrt(1-x^(2)))) w.r.t. cos^(-1)x^(2) .

If y = tan ^ (- 1) ((3x) / (1-2x ^ (2))), - (1) / (sqrt (2))

If y="tan"^(-1) (sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2))+sqrt(1-x^(2))) show that, (dy)/(dx)=(x)/(sqrt(1-x^(4)))

Evaluate: int_-(1/sqrt(3))^(1/sqrt(3)) (cos^-1((2x)/(1+x^2))+tan^-1((2x)/(1-x^2)))/(e^x+1)dx

Evaluate: int_-(1/sqrt(3))^(1/sqrt(3)) (cos^-1((2x)/(1+x^2))+tan^-1((2x)/(1-x^2)))/(e^x+1)dx

Evaluate: int_-(1/sqrt(3))^(1/sqrt(3)) (cos^-1((2x)/(1+x^2))+tan^-1((2x)/(1-x^2)))/(e^x+1)dx