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`sqrt(1-4x-x^(2))`

(1)/(sqrt(21+4x-x^(2)))

Integrate the following with respect to x : (i) (2x+1)/(sqrt(9+4x-x^2)) (ii) (x+2)/(sqrt(x^2-1)) (iii) (2x+3)/(sqrt(x^2+4x+1))

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

(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

Evaluate (x^2 - sqrt(1 - x^2) )^4 + (x^2 + sqrt( 1- x^2) )^4

int(x^2-1)/(x^3sqrt(2x^4-2x^2+1))dx is equal to (a) (sqrt(2x^4-2x^2+1))/(x^3)+C (b) (sqrt(2x^4-2x^2+1))/x+C (c) (sqrt(2x^4-2x^2+1))/(x^2)+C (d) (sqrt(2x^4-2x^2+1))/(2x^2)+C

int(x^2-1)/(x^3sqrt(2x^4-2x^2+1))dx is equal to (a) (sqrt(2x^4-2x^2+1))/(x^3)+C (b) (sqrt(2x^4-2x^2+1))/x+C (c) (sqrt(2x^4-2x^2+1))/(x^2)+C (d) (sqrt(2x^4-2x^2+1))/(2x^2)+C

int(x^2-1)/(x^3sqrt(2x^4-2x^2+1))dx is equal to (a) (sqrt(2x^4-2x^2+1))/(x^3)+C (b) (sqrt(2x^4-2x^2+1))/x+C (c) (sqrt(2x^4-2x^2+1))/(x^2)+C (d) (sqrt(2x^4-2x^2+1))/(2x^2)+C

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