" 37."(x^(3)sin(tan^(-1)x^(4)))/(1+x^(3))

(x^3sin(tan^(- 1)x^4))/(1+x^8)

Evaluate int(4x^(3)sin(tan^(-1)(x^(4))))/(1+x^(8))dx

(x ^ (3) sin (tan ^ (- 1) x ^ (4))) / (1 + x ^ (8))

Prove that: i) sin^(-1)(3x-4x^(3))=3sin^(-1)x, |x| le 1/2 ii) cos^(-1)(4x^(2)-3x)=3cos^(-1)x,1/2 le x le 1 iii) tan^(-1)""(3x-x^(3))/(1-3x^(2))=3tan^(-1)x, |x| lt 1/sqrt(3) iv) tan^(-1)x+tan^(-1)""(2x)/(1-x^(2))=tan^(-1)""(3x-x^(3))/(1-3x^(2))

int(x^(4)+1)/(x^(6)+1)dx(1)tan^(-1)x-tan^(-1)x^(3)+c(2)tan^(-1)x-(1)/(3)tan^(-1)x^(3)+c(3)tan^(-1)x+tan^(-1)x^(3)+c(4)tan^(-1)x+(1)/(3)tan^(-1)x^(3)+c

Solve for real values of x:((sin^(-1)x)^(3)+(cos^(-1)x)^(3))/((tan^(-1)x+cot^(-1)x)^(3))=7

Evaluate: (i) cot((sin^(-1)3)/(4)+(sec^(-1)4)/(3))( ii) sin(tan^(-1)x+(tan^(-1)1)/(x)) for x<0

Evaluate: (i) cot(sin^(-1)(3/4)+sec^(-1)(4/3)) (ii) sin(tan^(-1)x+tan^(-1)(1/x)) for x<0

If y = tan^(-1)((3x-x^(3))/(1-3x^(2))) + tan^(-1) ((4x-4x^(3))/(1-6x^(2) + 4x^(4))) then (dy)/(dx) =

IF 3 sin^(-1)((2x)/(1+x^(2)))-4cos^(-1)((1-x^(2))/(1+x^(2)))+ 2tan^(-1)((2x)/(1-x^(2)))=(pi)/3 then x=