If `I_(1)=int_(0)^(1)(dx)/(e^(x)(1+x))` and `I_(2)=int_(0)^(pi//4)(e^(tan^(7)theta)sintheta)/((2-tan^(2)theta)cos^(3)theta d theta`,then find the value of `(l_(1))/(l_(2))`.

If I_(1)=int_(0)^(1)(dx)/(e^(x)(1+x)) and I_(2)=int_(0)^(pi//4)(e^(tan^(2)theta)sintheta)/((2-tan^(2)theta)cos^(3)theta) d theta ,then find the value of (l_(1))/(l_(2)) .

int_(-pi/4) ^(pi/4) (e^theta(thetasintheta))/(e^(2theta)-1)d theta=

int_(0)^(pi//2) (sin^(2)theta)/ (1+cos theta)^(2) d theta =

If I_(1)=int_(0)^(1)(dx)/(e^(x)(1+x)) and I_(2)=int_(0)^( pi/2)(e^(sin^(2)theta)sin theta cos theta d theta)/((2-sin^(2)theta)) then (where [ .] denotes greatest integer function)

I=int_(0)^( pi/4)(sin2 theta)/(sin^(2)theta+cos^(4)theta)d theta

Evaluate: int_(0)^((pi)/(4))(tan^(-1)((2cos^(2)theta)/(2-sin2 theta)))sec^(2)theta d theta

Evaluate: int_0^(pi/4)(tan^(-1)((2cos^2theta)/(2-sin2theta)))sec^2thetad theta .

Evaluate: int_0^(pi/4)(tan^(-1)((2cos^2theta)/(2-sin2theta)))sec^2thetad theta

Evaluate: int_0^(pi/4)(tan^(-1)((2cos^2theta)/(2-sin2theta)))sec^2thetad theta .

Evaluate: int_0^(pi/4)(tan^(-1)((2cos^2theta)/(2-sin2theta)))sec^2theta d theta dot