`sqrt(81 + (2x + 1)^(2))`

Prove that sin^(-1). ((x + sqrt(1 - x^(2))/(sqrt2)) = sin^(-1) x + (pi)/(4) , where - (1)/(sqrt2) lt x lt(1)/(sqrt2)

Integrate the following with respect to x. (i) 1/(1 + (2x)^2) " " (ii) 1/(sqrt(1 - (9x)^2)) " " (iii) 1/(sqrt(1 - 25x^2)) .

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

Prove that sin [2 tan^(-1) {sqrt((1 -x)/(1 + x))}] = sqrt(1 - x^(2))

The number of solutions of the equation sqrt(x^(2))-sqrt((x-1)^(2))+sqrt((x-2)^(2))=sqrt(5) is

Find the value of x for which f(x) = 2 sin^(-1) sqrt(1 - x) + sin^(-1) (2 sqrt(x - x^(2))) is constant

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 (C) sqrt(x^2 + 1/x^2 + 1) + c (D) sqrt((x^4-x^2+1)/x) + c

Integrate (8)/(sqrt(1-(4x)^(2)))+(27)/(sqrt(1-9x^(2)))-(15)/(1+25x^(2)) with respect to x .