[" 3."x^(2)e^(x)],[" 7."x sin^(-1)x]quad 8" ."x tan^(-1)x

int (e^(x) (x^(2) tan^(-1) x + tan^(-1) x + 1))/( x^(2) + 1) dx is

If y = tan^(-1) ((1)/(1 + x + x^(2))) + tan^(-1) ((1) /(x^(2) + 2x + 3)) + tan^(-1) ((1)/(x^(2) + 5x + 7)) + ….n terms , then y(0) is

Let |{:(tan^(-1)x, tan^(-1)2x, tan^(-1)3x), (tan^(-1)3x, tan^(-1)x, tan^(-1)2x), (tan^(-1)2x, tan^(-1)3x, tan^(-1)x):}|=0 , then the number of values of x satisfying the equation is

If Delta(x) = |{:(x ,, 1+ x^(2) ,, x^(3)), ("log" (1+ x ^(2)) ,, e^(x) ,, sin x), ( cos x ,, tan x , , sin^(2)x):}| , then-

(3 pi)/(2) The value of int_(0)^((3 pi)/(2))(|tan^(-1)tan x|-|sin^(-1)sin x|)/(|tan^(-1)tan x|+|sin^(-1)sin x|)dx is equal to

int(2e^(5x)+e^(4x)-4e^(3x)+4e^(2x)+2e^(x))/((e^(2x)+4)(e^(2x)-1)^(2))dx= a) "tan"^(-1)(e^(x))/(2)-(1)/(e^(2x)-1)+C b) "tan"^(-1)e^(x)-(1)/(2(e^(2x)-1))+C c) "tan"^(-1)(e^(x))/(2)-(1)/(2(e^(2x)-1))+C d) 1-"tan"^(-1)((e^(x))/(2))+(1)/(2(e^(2x)-1))+C

If f(x) = frac{sin^(-1)x}{sqrt (1-x^2)} , g(x)=e^(sin^(-1)x) , then int f(x)g(x) dx =........................ A) e^(sin^(-1)x) (sin^(-1)x-1) + c B) e^( sin^(-1)x) (1- sin^(-1)x) + c C) e^(sin^(-1)x) (sin^(-1)x+1) + c D) -e^(sin^(-1)x) (sin^(-1)x-1) + c

If sin^(4) x = 1 + tan^(8) x then x has