Anyone know how to solve the following problems?
∫(x-1) / (lnx) dx Limit 0≦x≦1
∫(x^Alpha)*lnx dx Limit 0≦x≦1
∫(sin x)^3 / (x^2) dx Limit 0≦x≦∞
∫((sin x )/ x) dx Limit 0≦x≦∞
2. (a) Evaluate ∫((sin x)^3) /((sin x)^3 + (cos x)^3) dx Limit 0≦x≦Pi/2
(b) What is the rate of change of f(x) = arctan (tan x) at x =Pi/2
3. A point mass m moves along the curve y = 2(X^2) due to gravity and no other external force is present. Determine the power of gravity as a function of Xo, g, t. (Xo means x knot)