Evaluate `I=int 1/sint.dt`

Evaluate indefinite integration. (i) x=intdt " " (ii) int t dt " " (iii) x=int (2t) dt" " (iv) x=int (t^(2)) dt " " (v) x=int (-(2)/(t^3))dt

Evaluate int^t _0 A sin omega dt where A and omega are constants.

Evaluate int(t^(2))/(sqrt(1-t^(2)))dt

If int_(0)^(1)(sint)/(1+t)dt=alpha , them the value of the integral int_(4pi-2)^(4pi)("sin"(t)/(2))/(4pi+2-t)dt in terms of alpha is given by

Evaluate (i) int_(-2)^(1)(tan^(-1)x+cot^(-1).(1)/(x))dx (ii) int_(2)^(4)sqrt(t-1-2sqrt(t-2))dt .

Evaluate int_(0)^(oo)(dt)/(t)

Evaluate the integral : (i) int_(1)^(5) x^(2)dx " " (ii) int_(0)^(1) t^(2)dt" " (iii) int_(3)^(5) t dx " " (iv) int_(0)^(1) t^(3//2)dx

int_(0)^( If )(f(t))dt=x+int_(x)^(1)(t^(2)*f(t))dt+(pi)/(4)-1 then the value of the integral int_(-1)^(1)(f(x))dx is equal to