If `I = int_2^3((x-1)^3 + (4-x)^3+ x) cos pixdx` , then `| 50pi^2 I|` is equal to

If I = int(2cos^(2)x-1)(4cos^(3)x-3cosx)dx=Asin5x+(1)/(2)sinx+C then A is equal to

If I_(1) = int_(0)^(pi) (x sin x)/(1+cos^2x) dx , I_(2) = int_(0)^(pi) x sin^(4)xdx then, I_(1) : I_(2) is equal to

If I_(1) = int_(0)^(pi) (x sin x)/(1+cos^2x) dx , I_(2) = int_(0)^(pi) x sin^(4)xdx then, I_(1) : I_(2) is equal to

If I_(n)=int_(0)^( pi)e^(x)(sin x)^(n)dx, then (I_(3))/(I_(1)) is equal to

If I_(n)=int_(0)^(pi) e^(x)sin^(n)x " dx then " (I_(3))/(I_(1)) is equal to

int_(-3pi//2)^(-pi//2) [(x +pi)^3 + cos^2 (x + 3pi)]dx is equal to :

(i) int x^3 sin x^2 dx (ii) int x^3 cos x^2 dx

If I_(1) int sin^(-1) ((2x)/(1 +x^(2)) ) dx , I_(2) = int cos^(-1) ((1-x^(2))/(1 +x^(2)) ) dx , I_(3) = int tan^(-1) ((2x)/(1 - x^(2)) ) dx , then I_(1) + I_(2) - I_(3) =

If I=int_(0)^((3 pi)/(5))(1+x)sin x+(1-x)cos x)dx then value of (sqrt(2)-1)I is