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

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

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

int(x^(3)sin[tan^(-1)(x^(4))])/(1+x^(8))dx=

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

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

Prove that tan^(-1)((6x-8x^(3))/(1-12x^(2)))-tan^(-1)((4x)/(1-4x^(2)))=tan^(-1)2x;|2x|<(1)/(sqrt(3))

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))

Range of the function f(x)=sin^(-1)x+2tan^(-1)x+x^(2)+4x+3 is

If the integral int_(sin^(-1)(sin8))^(tan^(-1)(tan8))(sin^(3)(x^(5))+sin^(5)(x^(3)))/(cos^(6)x+cos^(8)x)dx has the value lambda ; then the least prime number greater than lambda is