Prove that the function L(x) defined on the interval (0,infty) by the integral L(x) = int_(1)^(x) (dt)/(t) possesses the following properties. L(x_(1)x_(2)) = L(x_(1)) + L(x_(2)) L((x_(1))/(x_(2))) = L(x_(1)) - L(x_(2))
The greatest integral value of m for which the point of intersection of L_1 : 2x+y=50 a n d L_2 : y=mx+1 has integral coordinate, is a. 5 b. 9 c. 47 d. 51""
Square of the distance between the integral points of intersection of L_1a n dL_2 for the greatest and the least integral values of m is 5 b. 20 c. 25 d. 30""
Integration OF Rational || Integration OF Irrational function || Integration OF [ ( x^2 + 1) || Integration OF ( x^4+k x^2+1) ] type || Illustration
Integrate tan^-1x
Integrate the function tan^(-1) √(1-x)/(1+x)
Integrate the functions (1-cos x)/(1+cos x)
Integrate: x^2- cos x + (1/x) .
If the integral l_(n)=int_(0)^(pi//4)tan^(n)xdx is reduced to its lower integrals like l_(n-1),l_(n-2) etc., The value of (l_(3)+2l_(5))/(l_(1)) is
