int(x^(3))/(x^(4)+x^(2)+1)dx=pi

int_(0)^(1)x.sqrt((1-x^(2))/(1+x^(2)))dx=(pi-2)/(4)

STATEMENT-1 : int_(0)^(oo)(dx)/(1+e^(x))=ln2-1 STATEMENT-2 : int_(0)^(oo)(sin(tan^(-1)))/(1+x^(2))dx=pi STATEMENT-3 : int_(0)^(pi^(2)//4)(sinsqrt(x))/(sqrt(x))dx=1

STATEMENT-1 : int_(0)^(oo)(dx)/(1+e^(x))=ln2-1 STATEMENT-2 : int_(0)^(oo)(sin(tan^(-1)))/(1+x^(2))dx=pi STATEMENT-3 : int_(0)^(pi^(2)//4)(sinsqrt(x))/(sqrt(x))dx=1

Prove that int_(0)^(pi)(xsin^(3)x)/(1+cos^(2)x)dx=pi/2(pi-2)

7(int_(0)^(1)(x^(4)(1-x)^(4)dx)/(1+x^(2))+pi) is equal to

int_(-pi/2)^(pi/2) sin^(8) x (6x^(7)-4x^(5)+3x^(3)+2x) dx =

The value of int_(0)^(oo)(dx)/(1+x^(4)) is (a) same as that of int_(0)^(oo)(x^(2)+1dx)/(1+x) (b) (pi)/(2sqrt(2))( c) same as that of int_(0)^(oo)(x^(2)+1dx)/(1+x^(4))(d)(pi)/(sqrt(2))

Show that int_(0)^((pi)/(2))(tan^(4)x)/(1+tan^(4)x)dx=(pi)/(4)

int_(0)^( pi)(x)/((1+x)(1+x^(2)))dx

int_(-pi//4)^(pi//4)(e^(x)(x^(3)sinx))/(e^(2x)-1)dx equals