[" 42."int(x^(2)-1)/((x^(2)+1)sqrt(x^(4)+1))dx=],[" (a) "sec^(-1)((x^(2)+1)/(sqrt(2)x))+c" (b) "(1)/(sqrt(2))sec^(-1)((x^(2)+1)/(sqrt(2)x))+c],[" (c) "(1)/(sqrt(2))sec^(-1)((x^(2)+1)/(sqrt(2)))+cquad " (d) None "]

int(x^(4)-1)/(x^(2))sqrt(x^(4)+x^(2)+1)dx equal to (A) sqrt((x^(4)+x^(2)+1)/(x)+c(B)sqrt(x^(4)+2-(1)/(x^(2)))+c)sqrt((x^(4)-x^(2)+1)/(x))+c

int(dx)/(e^(x)sqrt(2e^(x)-1))=2sec^(-1)sqrt(2e^(x))+c-2tan^(-1)(1)/(sqrt(2e-1))+c2sec^(-1)(sqrt(2)e^(x))+c(d)2tan^(-1)sqrt(2e^(x)-1)+c

int (dx)/(sqrt(2e^(x)-1))=2 sec^(-1)(sqrt(2)e^((x)/(2)))+c

The value of integral inte^x(1/(sqrt(1+x^2))+(1-2x^2)/(sqrt((1+x^2)^5)))dx is equal to (a)e^x(1/(sqrt(1+x^2))+x/(sqrt((1+x^2)^3)))+c (b)e^x(1/(sqrt(1+x^2))-x/(sqrt((1+x^2)^3)))+c (c)e^x(1/(sqrt(1+x^2))+x/(sqrt((1+x^2)^5)))+c (d)none of these

The value of integral inte^x(1/(sqrt(1+x^2))+(1-2x^2)/(sqrt((1+x^2)^5)))dx is equal to (a)e^x(1/(sqrt(1+x^2))+x/(sqrt((1+x^2)^3)))+c (b)e^x(1/(sqrt(1+x^2))-x/(sqrt((1+x^2)^3)))+c (c)e^x(1/(sqrt(1+x^2))+x/(sqrt((1+x^2)^5)))+c (d)none of these

int(x^(4)-1)/(x^(2)sqrt(x^(2)+x^(2)+1))dx=sqrt(x^(2)+(1)/(x^(2))+1)+C(sqrt(x^(2)+x^(2)+1))/(x^(2))+C(sqrt(x^(4)+x^(2)+1))/(x)+C(d) none of these

(d)/(dx)[cos^(-1)(x sqrt(x)-sqrt((1-x)(1-x^(2))))]=(1)/(sqrt(1-x^(2)))-(1)/(2sqrt(x-x^(2)))(-1)/(sqrt(1-x^(2)))-(1)/(2sqrt(x-x^(2)))(1)/(sqrt(1-x^(2)))+(1)/(2sqrt(x-x^(2)))(1)/(sqrt(1-x^(2)))0 b.1/4c.-1/4d none of these

d/(dx){sec^(-1)""(1)/(sqrt(1-x^2))+cot^(-1)""(sqrt(1-x^2))/x} =

The value if int(x^(2)-1)/((x^(2)+1)(sqrt(x^(4)+1)))dx equal to (1)/(sqrt(2))sec^(-1)(f(x))+c , then f(x) is